The *[Center for Quantum and Topological Systems](https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts.html)* ([nyuad.nyu.edu/L.cqts](https://nyuad.nyu.edu/cqts))  is a Research Center, launched in 2022, within the [Research Institute](https://nyuad.nyu.edu/en/research/research-institute-centers.html) of [New York University in Abu Dhabi](https://nyuad.nyu.edu/en/).

[CQTS](https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/center-for-quantum-and-topological-systems.html) hosts cross-disciplinary research on *[[topological physics -- contents|topological]] [[quantum systems]]*,  such as [[topological phases of matter]] understood [[AdS-CFT in condensed matter physics|via holography]] and using tools from [[algebraic topology]], ultimately aimed at addressing open questions in [[topological quantum computation|topological]] [[quantum computation]]. A unifying theme is the use of new methods from ([[persistent cohomotopy|persistent]]) *[[Cohomotopy]]* ([[schreiber:M/F-Theory as Mf-Theory|aka]] *[[framed manifold|framed]] [[cobordism cohomology|Cobordism]]*, [aka](stable+cohomotopy#AsAlgebraicKTheoryOverTheFieldWithOneElement) *[[field with one element|absolute $\mathbb{F}_1$]]-[[algebraic K-theory]]*) and [[generalized cohomology|generalized]] [[twisted cohomology|Twisted]] [[equivariant cohomology|Equivariant]] [[differential cohomology|Differential]] ([[schreiber:Twisted Equivariant Differential non-abelian generalized cohomology|TED]]) [[cohomology]], developed [[Hypothesis H|in string theory]].

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#Contents#
* table of contents
{:toc}

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## Conferences & Workshops

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***

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### Jun 2022
 {#MeetingsJune2022}

  **[[homotopy theory|Homotopical]] perspectives on [[topological data analysis|Topological data analysis]]
  {#HomotopicalPerspectivesOnTDAJune2022}

  Organizers: [[Sadok Kallel]] and [[Hisham Sati]]

  \linebreak

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  \linebreak

  Schedule for **02 June 2022**:

  \linebreak

  * 15:00 - 16:00 [GST/UTC+4](https://www.timeanddate.com/time/zones/gst)
    {#ZhouAtHomotopicalPerspectivesOnTDAJune2022}

    [[Ling Zhou]] (The Ohio State University, USA)

    **Persistent homotopy groups of metric spaces**

    > By capturing both geometric and topological features of datasets, [[persistent homology]] has shown its promise in applications. Motivated by the fact that [[homotopy]] in general contains more information than [[homology]], we study notions of [[persistent homotopy]] groups of compact [[metric spaces]], together with their stability properties in the Gromov-Hausdorff sense. Under fairly mild assumptions on the spaces, we proved that the classical [[fundamental group]] has an underlying tree-like structure (i.e. a dendrogram) and an associated ultrametric. We then exhibit pairs of filtrations that are confounded by [[persistent homology]] but are distinguished by their [[persistent homotopy]] groups. We finally describe the notion of persistent [[rational homotopy theory|rational]] homotopy groups, which is easier to handle but still contains extra information compared to persistent homology.

    \linebreak

  * 16:00 - 17:00 [GST/UTC+4](https://www.timeanddate.com/time/zones/gst)

    [[Wojciech Chacholski]]  (KTH, Sweden)
      {#ChacholskiTalkAtHomotopicalPerspectivesOnTDA2022}

    **Realisations of Posets**

    > My presentation  is based on an article with the same title coauthored with A. Jin and F. Tombari  ([arXiv:2112.12209](https://arxiv.org/abs/2112.12209)).

    > Encoding information in form of  [[functors]] indexed by the [[poset]] of $r$-tuples of real numbers ([[persistence modules]]) is attractive for three reasons:

    > a) metric properties  of the poset are essential  to study  distances on persistence modules

    > b) the poset of $r$-tuples of real numbers has well behaved discrete  approximations which are  used  to provide finite  approximations of  persistence modules

    > c) the mentioned discretizations and approximations  have well studied algebraic and homological properties as they can be identified with  multi graded modules over polynomial rings.

    > In my talk I will describe a construction called realisation, that transforms arbitrary posets into posets  which satisfy all three requirements above and hence  are particularly suitable for persistence methods.Intuitively the realisation associates a continuous structure to a locally discrete poset by filling in empty spaces. For example the realisation of the poset of natural numbers is the poset of non-negative reals. I will focus on illustrating how [[homological algebra|homological techniques]], such as [[Koszul complexes]], can be used to study [[persistence modules]] indexed by realisations.

    \linebreak

  * 17:30 - 18:30 [GST/UTC+4](https://www.timeanddate.com/time/zones/gst)
    {#GinotAtHomotopicalPerspectivesOnTDAJune2022}

    [[Grégory Ginot]]  (Université Paris 13, France)

    **Homotopical and sheaf theoretic point of view on multi-parameter persistence. **

    >  In this talk we will highlight the study of [[level set]] [[persistent homology|persistence]] through the prism of [[sheaf theory]] and a special type of 2-parameter persistence: Mayer-Vietoris systems and a pseudo-symetry between those. This is based on [joint work with Berkouk and Oudot](persistent+homology#BerkoukGinotOudot19).

    \linebreak

  * 18:30 - 19:30 [GST/UTC+4](https://www.timeanddate.com/time/zones/gst)
    {#JardineAtHomotopicalPerspectivesOnTDAJune2022}

    [[Rick Jardine]]  (University of Western Ontario, Canada)

    **Thoughts on big data sets**

    > This talk describes work in progress. The idea is to develop methods for analyzing a very large data sets $X \subset \mathbb{R}^{N}$ in high dimensional spaces. There are well-known pitfalls to avoid, including the inability to computationally analyze [[TDA]] constructions for $X$ on account of its size, the "curse of high dimensionality", and the failure of [[excision]] for standard [[TDA]] constructions. We discuss the curse of high dimensionality and define a hypercube metric on $\mathbb{R}^{N}$ that may lessen its effects. The excision problem for the [[Vietoris-Rips complex|Vietoris-Rips construction]] can be addressed by expanding the [[TDA]] discussion to [[filtered object|filtered]] subobjects $K$ of Vietoris-Rips constructions. Unions of such subobjects satisfy excision in path components (clusters) and [[homology groups]], by classical results. The near-term goal is to construct, for each data point $x$, a "computable" filtered subcomplex $K_{x} \subset V(X)$ with $x \in K_{x}$, which would capture spatial local behaviour of the data set $X$ near $x$. A large (but highly parallelizable) algorithm finds a nearest neighbour, or a set of $k$-nearest neighbours for a fixed data point $x \in X$. Some variant of this algorithm may lead to a good construction of the local subcomplex $K_{x}$.

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### Jan 2023

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* 12-15 Jan 2023

  **[M-Theory and Mathematics 2023](M-Theory+and+Mathematics#2023)** -- *Classical and Quantum Aspects*

  > on [[M-theory]] ([[non-perturbative]] [[string theory]] and related [[quantum field theories]])

> $\phantom{-----}$ [logo adapted from [JMP **62** (2021) 042301](/schreiber/show/Twisted+Cohomotopy+implies+twisted+String+structure+on+M5-branes)]

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### Feb 2023

{#CQTSandTIIWorkshopFeb2023}  24 Feb 2023

**CQTS and TII Workshop** 2023

joint workshop with the [Quantum Research Center](https://www.tii.ae/quantum) (QRC) at the [Technology Innovation Institute](https://www.tii.ae/) (TII) in Abu Dhabi

> on [[quantum materials]], [[quantum computation]] and [[quantum programming]]

* 9:00 - 9:05

  [[Hisham Sati]]:

  **Welcome**

* 9:05 - 9:15

  [[Luigi Amico]]:

  **Introduction to [Quantum Physics @ TII](https://www.tii.ae/quantum)**

* 9:20 - 9:45

  [[Juan Polo Gomez]]:

  **[[atomtronics|Atomtronics]]**

* 9:50 - 10:10

  [Enrico Domanti](https://www.tii.ae/team/enrico-domanti):

  **Coherence of confined matter in [[lattice gauge theories]] at the mesoscopic scale**

* 10:15 - 10:40

  [[Gianluigi Catelani]]:

  **[Superconducting qubits](superconductivity#SuperconductingQBitsReferences)**

Break: 10:40 - 11:10

* 11:10 - 11:15

  [[Leandro Aolita]]:

  **Intro to Quantum Algorithms @TII**

* 11:20 - 11:50

  [[Ingo Roth]]:

  **[Quantum device characterization](certified+programming#QuantumHardwareVerification)**

* 11:55 - 12:25

  Egor Tiunov:

  **Quantum-inspired algorithms**

* 12:30 - 13:00

  Thais de Lima Silva:

  **Quantum algorithms: Quantum Signal Processing**

Lunch: 13:00 – 2:15

* 14:15 - 14:25

  [[Hisham Sati]]:

  **Introducing research and researchers @CQTS**

* 14:30 - 14:50

  [[Amaria Javed]]:

  **Quantum information processing via NLS**

* 15:00 - 15:20

  [[Marwa Mannaï]]:

  **Tuning topological quantum materials**

* 15:30 - 15:50

  [[Mitchell Riley]]:

  **Verified quantum programming with linear HoTT**

Break: 3:50-4:20 pm

* 4:20 - 4:40

  [[Vivek Singh]]:

  **Topological Quantum field theory for TQC**

* 16:50 - 17:10

  [[Sachin Valera]]:

  **Topological Qubits from Anyons**

* 17:20 - 17:50

  [[Urs Schreiber]]:

  **[Towards verified hardware-aware topological quantum programming](https://ncatlab.org/schreiber/show/Topological+Quantum+Gates+in+Homotopy+Type+Theory#TalkForTII)**

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### Mar 2023
 {#ConferencesMar2023}

15-18 Mar 2023

**Geometric/Topological Quantum Field Theories and Cobordisms** ([webpage](https://nyuad.nyu.edu/en/events/2023/march/quantum-field-theories-and-cobordisms.html))

> on [[functorial quantum field theory]], [[knot homology]] and [[cobordism theory]]/[[cobordism categories]]/[[cobordism hypothesis]]

> $\phantom{-----}$ [logo adapted from [[schreiber:M/F-Theory as Mf-Theory|arXiv:2103.01877]]]

{#QFTandCobordism2023GroupPhoto} $\;\;$

[[Mee Seong Im]], [[Mikhail Khovanov]], [[Vivek Singh]], [[Sergei Gukov]], [[Anna Beliakova]],  [Khaled Qazaqzeh](https://math.sci.kuniv.edu.kw/people/faculty/khaled-qazaqezeh)

[[Domenico Fiorenza]], [[Carlo Collari]], [[Sadok Kallel]], [[Nafaa Chbili]], [[Christian Blanchet]], [[David Jaz Myers]]

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ [[Nitu Kitchloo]], [[Daniel Berwick-Evans]], [[Adrian Clough]]

[[Sachin Valera]], [[Alonso Perez-Lona]], [[Urs Schreiber]] $\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ [[Daniel Grady]], [[Christoph Schweigert]]

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ [[Hisham Sati]], [[Konrad Waldorf]], [[Dmitri Pavlov]]

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* {#KhovanovMar2023} [[Mikhail Khovanov]] (Columbia University):

  **Universal construction, foams and link homology**

  cf.: [arXiv:1808.09662](https://arxiv.org/abs/1808.09662), [arXiv:2011.11077](https://arxiv.org/abs/2011.11077)

  video 1:[YT](https://www.youtube.com/watch?v=Urh1NNcbCcc), 2:[YT](https://www.youtube.com/watch?v=SPBcAAmGT88)

  > In this series of three talks we will explain the foam approach to [[link homology]]. Bigraded link homology theories [[categorification|categorify]] the [[Jones polynomial]] and other [[Reshetikhin-Turaev construction|Reshetikhin-Turaev]] [[link invariants]], such as the [[HOMFLY-PT polynomial]]. Foams, which are [[polyhedron|polyhedral]] 2D [[cell complex|complexes]] embedded in [[Euclidean space|3-space]] allow to construct state spaces for [[planar graphs]] which are then used to define link homology groups. The most explicit and efficient way to define graph state spaces is via evaluation of the closed foams (Robert-Wagner formula).

  > A) This formula will be first explained in the less technical unoriented $SL(3)$ case. Resulting graph state spaces are then related to the Four-Color Theorem and Kronheimer-Mrowka homology for 3-[[orbifolds]].

  > B) A step in that construction requires building a topological theory (a lax TQFT) from an evaluation of closed objects, such as closed $n$-manifolds. We will explain the setup for topological theories, including in two dimensions, recovering the Deligne categories and their generalizations. In one dimension and adding defects, these topological theories are related to noncommutative power series, pseudocharacters, and, over the Boolean semiring, to [[regular languages]] and [[automata]].

  > C) Robert-Wagner $GL(N)$ foam evaluation and its application to constructing link homology theories will be explained as well.

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* {#KitchlooMar2023} [[Nitu Kitchloo]] (John Hopkins University):

  **Symmetry breaking and homotopy types for link homologies**

  cf.: [arXiv:1910.07443](https://arxiv.org/abs/1910.07443), [arXiv:1910.07444](https://arxiv.org/abs/1910.07444), [arXiv:1910.07516](https://arxiv.org/abs/1910.07516)

  video: [YT](https://www.youtube.com/watch?v=StRyIjpER9I)

  > I will describe how the spaces that record [[symmetry breaking]] data in a $U(n)$-[[gauge theory]] (for arbitrary $n$) can be used to construct [[homotopy types]] that are [[link invariant|invariants for links]] in $\mathbb{R}^3$. In particular, I will show how one may recover [[Khovanov-Rozansky link homology]] and $\mathfrak{sl}(n)$ [[link homology]] by evaluating this homotopy type under suitable [[Whitehead-generalized cohomology|cohomology theories]].

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* {#GukovMar2023} [[Sergei Gukov]] (DIAS, Dublin and Caltech)

  **Machine learning and hard problems in topology**

  cf.: [arXiv:2010.16263](https://arxiv.org/abs/2010.16263)

  slides: [[Gukov-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=dHkGJIP1u4U)

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* {#CarquevilleMar2023} [[Nils Carqueville]] (University of Vienna):

  **Truncated Rozansky-Witten models as extended defect TQFTs**

  slides: [pdf](https://www.carqueville.net/nils/RW.pdf), [[Carqueville-RW.pdf:file]]

  cf.: [arXiv:2201.03284](https://arxiv.org/abs/2201.03284)

  video: [YT](https://www.youtube.com/watch?v=bwDJSitenVE)

  > According to the [[cobordism hypothesis]] with singularities, fully [[extended topological quantum field theories]] with [[defect QFT|defects]] are equivalently described in terms of coherent full duality data for objects and (higher) morphisms as well as appropriate [[homotopy fixed point]] [[structures]]. We discuss the 2-dimensional oriented case in some detail and apply it to truncated affine [[Rozansky-Witten theory|Rozansky-Witten models]], which are under very explicit computational control. This is joint work with [[Ilka Brunner]], [Pantelis Fragkos](https://www.theorie.physik.uni-muenchen.de/MATH/members/asc/sci_mem/fragkos_pantelis/index.html), and [[Daniel Roggenkamp]].

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* {#DebrayMar2023} [[Arun Debray]] (Purdue University):

  **Twisted string bordism and a potential anomaly in $E_8 \times E_8$ heterotic string theory**

  cf.: [arXiv:2210.04911](https://arxiv.org/abs/2210.04911)

  video: [YT](https://www.youtube.com/watch?v=wkucLJ7jTlM)

  > [[quantum field theory|Quantum field theories]] can have an inconsistency called an [[quantum anomaly|anomaly]], formulated as an [[invertible field theory]] in one dimension higher. Theorems of Freed-Hopkins-Teleman and [Freed-Hopkins](invertible+field+theory#FreedHopkins21) classify [[invertible field theories]] in terms of [[bordism groups]]. In this talk, I'll apply this to the low-energy approximation of $E_8 \times E_8$ [[heterotic string theory]]; Witten proved anomaly cancellation in a restricted setting, but we perform a twisted string bordism computation to show that the relevant group of 11-dimensional [[invertible field theories]] does not vanish, and therefore there could be an anomaly in $E_8 \times E_8$ heterotic string theory. Standard computational techniques for twisted [[string bordism]] do not work for this problem; I will also discuss work joint with Matthew Yu using Baker-Lazarev's R-module Adams spectral sequence to simplify a large class of twisted spin and string bordism computations.

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* {#YoungMar2023} [[Matthew Young]] (Utah State University):

  **Non-semisimple TFT and $U(1 \vert 1)$ Chern-Simons theory**

  cf.: [arXiv:2210.04286](https://arxiv.org/abs/2210.04286) and *[[super Chern-Simons theory]]*

  slides: [[Young-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=m73KQCwXOrY)

  > [[Chern-Simons theory]], as [introduced by Witten](Chern-Simons+theory#Witten89), is a three dimensional [[quantum field theory|quantum]] [[gauge theory]] associated to a [[compact Lie group|compact]] [[simple Lie group]] and a [[level (Chern-Simons theory)|level]]. The mathematical model of this theory as a [[topological field theory]] was introduced by [[Reshetikhin-Turaev construction|Reshetikhin and Turaev]] and is at the core of modern [[quantum topology]]. The goal of this talk is to explain a non-[[semisimple category|semisimple]] modification of the [[Reshetikhin-Turaev construction|construction of Reshetikhin and Turaev]] which realizes Chern-Simons theory with gauge [[supergroup]] $U(1\vert 1)$, as studied in the physics literature by Rozansky-Saleur and Mikhaylov. The key new algebraic structure is a relative [[modular tensor category|modular structure]] on the [[category of representations]] of the [[quantum group]] of $\mathfrak{gl}(1\vert 1)$. Based on joint work with [[Nathan Geer]].

\linebreak

* {#ImMar2023} [[Mee Seong Im]] (United States Naval Academy):

  **Correspondence between automata and one-dimensional Boolean topological theories and TQFTs**

  cf.: [arXiv:2301.00700](https://arxiv.org/abs/2301.00700)

  video: [YT](https://www.youtube.com/watch?v=q5kynYxwTmk)

  > [[automata|Automata]] are important objects in theoretical [[computer science]]. I will describe how automata emerge from topological theories and [[TQFTs]] in dimension one and carrying [[defect QFT|defects]]. Conversely, given an automaton, there's a canonical Boolean TQFT associated with it. In those topological theories, one encounters pairs of a [[regular language]] and a circular regular language that describe the theory.

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* {#SchenkelMar2023} [[Alexander Schenkel]] (University of Nottingham):

  **Quantum field theories on Lorentzian manifolds**

  cf.: [arXiv:2208.04344](https://arxiv.org/abs/2208.04344) and  *[[homotopical AQFT]]*

  slides: [[Schenkel-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=YiQNAgcwZYQ)

  > This talk provides an introduction and survey of recent developments in [[AQFT|algebraic QFT]] on [[Lorentzian manifolds]]. I will outline an [[axiom|axiomatization]] of such [[QFTs]] in terms of [[operad]] theory and illustrate this formalism through classification results in low dimensions. One of the central axioms is a certain local constancy condition, called the [[time-slice axiom]], that encodes a concept of time evolution. Using [[model category|model categorical]] [[localization of model categories|localization]] techniques, I will show that this i.g. [[homotopy]]-[[coherence|coherent]] time evolution admits a [[rectification|strictification]] in many relevant cases. I will conclude this talk by explaining similarities and differences between [[AQFT|algebraic QFT]] and other approaches such as [[factorization algebras]] and [[functorial field theories]].

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* {#WaldorfMar2023} [[Konrad Waldorf]] (University of Greifswald):

  **The stringor bundle**

  cf.: [arXiv:2206.09797](https://arxiv.org/abs/2206.09797)

  video: [YT](https://www.youtube.com/watch?v=wX99ZbMuyMA)

  >  The [[stringor bundle]] plays the role of the [[spinor bundle]], but in [[string theory]] instead of [[quantum mechanics]]. It has been anticipated in [[What is an elliptic object?|pioneering work of Stolz and Teichner]] as a [[vector bundle]] on [[loop space]]. I will talk about joint work with [[Matthias Ludewig]] and [[Peter Kristel]] that provides a fully rigorous and neat presentation of the stringor bundle as an associated 2-vector bundle, via a representation of the string 2-group on a [[von Neumann algebra]].

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* {#FiorenzaMar2023} [[Domenico Fiorenza]] (Sapienza University of Rome):

  **String bordism invariants in dimension 3 from $U(1)$-valued TQFTs**

  cf.: [arXiv:2209.12933](https://arxiv.org/abs/2209.12933)

  pdf: [[Fiorenza-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=6DUxyCgYFLw)

  > The third [[string bordism]] [[cohomology group|group]] [[third stable homotopy group of spheres|is known]] to be [[cyclic group|$\mathbb{Z}/$]][[24]]. Using [Waldorf's notion](differential+string+structure#Waldorf) of a [[geometric string structure]] on a manifold, Bunke-Naumann and Redden have exhibited integral formulas involving the [[Chern-Weil homomorphism|Chern-Weil form]] representative of the [[first Pontryagin class]] and the canonical 3-form of a [[geometric string structure]] that realize the [[isomorphism]] between the third [[string bordism]] group and $\mathbb{Z}/24$ (these formulas have been recently rediscovered by [[Davide Gaiotto|Gaiotto]], [[Theo Johnson-Freyd|Johnson-Freyd]] & [[Edward Witten|Witten]]). In the talk I will show how these formulas naturally emerge when one considers the $U(1)$-valued 3d [[TQFTs]] associated with the [[moduli stack|classifying stacks]] of [[spin bundle|Spin bundles]] [[connection on a principal bundle|with connection]] and of [[string 2-group|String]] [[principal 2-bundle|bundles]] with [[differential string structure|geometric structure]]. Joint work with [[Eugenio Landi]] ([arXiv:2209.12933](https://arxiv.org/abs/2209.12933)).

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* {#BlanchetMar2023} [[Christian Blanchet]] (Université Paris Cité):

  **Heisenberg homologies of surface configurations**

  cf.: [arXiv:2206.11475](https://arxiv.org/abs/2206.11475)

  slides: [[Blanchet-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=prcU4v7LFZQ)

  > The [[Heisenberg group]] of a [[surface]] is the [[central extension]] of its one-dimensional [[ordinary homology|homology]] associated with the [[intersection pairing|intersection cocycle]]. We show that a [[group representation|representation]] of the [[Heisenberg group]] defines [[local coefficients]] on the unordered [[configuration space of points]] in the surface. We study the corresponding [[ordinary homology|homologies]], the [[mapping class group|Mapping Class Group]] [[group action|action]] and the connection with quantum constructions. This is based on joint work with [[Awais Shaukat]] and [[Martin Palmer]].

\linebreak

* {#ChbiliMar2023} [[Nafaa Chbili]] (United Arab Emirates University):

  **Quasi-alternating links, Examples and obstructions**

  cf.: [arXiv:2009.08624](https://arxiv.org/abs/2009.08624)

  video: [YT](https://www.youtube.com/watch?v=1hd0vFxU2ro)

  > Quasi-alternating links represent an important class of [[links]] that has been [introduced by Ozsváth and Szabó](https://arxiv.org/abs/math/0309170) while studying the Heegaard Floer homology of the branched double-covers of alternating links. This new class of links, which share many [[Khovanov homology|homological properties]] with alternating links, is defined in a recursive way which is not easy to use in order to determine whether a given link is quasi-alternating. In this talk, we shall review the main obstruction criteria for quasi-alternating links. We also discuss how new examples of quasi-alternating links can constructed.

\linebreak

* {#QazaqzehMar2023} [Khaled Qazaqzeh](https://math.sci.kuniv.edu.kw/people/faculty/khaled-qazaqezeh) (Kuwait University):

  **On the Finiteness of Quasi-alternating Links**

  cf.: [arXiv:2208.02984](https://arxiv.org/abs/2208.02984)

  slides: [[Qazaqzeh-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=bUsCDAUiX60)

  > The generalization of alternating links to quasi-alternating links raises some natural questions that have affirmative answer in the class of alternating links.

  > In this talk, we discuss these questions and then we give an affirmative answer to one question without any assumption. As a consequence, we prove that one of these questions is solved in the affirmative iff Green's conjecture on the finiteness of quasi-alternating links of a given determinant holds.  Also, we prove that another question is solved in the affirmative implies Green's conjecture on the finiteness of quasi-alternating links of a given determinant holds.

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* {#PavlovMar2023} [[Dmitri Pavlov]] (Texas Tech University):

  **The geometric cobordism hypothesis**

  cf.: [arXiv:2011.01208](https://arxiv.org/abs/2011.01208), [arXiv:2111.01095](https://arxiv.org/abs/2111.01095)

  slides: [pdf](https://dmitripavlov.org/nyuad.pdf), [[Pavlov-GCHatCQTS.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=n6Eog_z82eA)

  > I will explain my recent joint work with [[Daniel Grady]] on [[local field theory|locality]] of [[functorial field theories]] ([arXiv:2011.01208](https://arxiv.org/abs/2011.01208)) and the [geometric cobordism hypothesis](cobordism+hypothesis#ReferencesGeometricCobordisms) ([arXiv:2111.01095](https://arxiv.org/abs/2111.01095)). The latter generalizes the Baez–Dolan [[cobordism hypothesis]] to non-[[topological field theories]], in which [[bordisms]] can be equipped with [[geometry|geometric]] [[structures]], such as [[smooth maps]] to a fixed [[target space|target]] [[smooth manifold|manifold]], [[Riemannian metrics]], [[conformal structures]], [[principal bundles]] [[connection on a bundle|with connection]], or [[geometric string structures]]. Applications include a generalization of the [Galatius–Madsen–Tillmann–Weiss theorem](cobordism+category#GMTWTheorem), a solution to a [[What is an elliptic object?|conjecture of Stolz and Teichner]] on [[representable functor|representability]] of [[concordance classes]] of [[functorial field theories]], and a construction of [[power operations]] on the level of [[functorial field theory|field theories]] (extending the [recent work of Barthel-Berwick-Evans-Stapleton](https://arxiv.org/abs/2006.09943)).

  > I will illustrate the general theory by constructing the [[prequantum field theory|prequantum]] [[Chern-Simons theory]] as a [[extended functorial field theory|fully extended]] nontopological [[functorial field theory]].

  > If time permits, I will discuss the ongoing work on defining [[quantization]] of field theories in the setting of the [geometric cobordism hypothesis](cobordism+hypothesis#ReferencesGeometricCobordisms).

\linebreak

* {#GradyMar2023} [[Daniel Grady]] (Wichita State University):

  **Deformation classes of invertible field theories and the Freed-Hopkins conjecture**

  slides: [[Grady-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=PzD6IDeLlS4)

  > In their [seminal paper](https://arxiv.org/abs/1604.06527), [Freed and Hopkins](#FreedHopkins21) proved a classification theorem that identifies [[deformation]] classes of certain [[invertible field theory|invertible]] [[topological field theories]] with the [[torsion subgroup]] of some [[Whitehead-generalized cohomology theory|generalized cohomology]] of a [[Thom spectrum]]. They [[conjecture|conjectured]] that the identification continues to hold for non-topological field theories, if one passes from the torsion subgroup to the full [[Whitehead-generalized cohomology|generalized cohomology group]] of the [[Thom spectrum]]. In this talk, I will discuss a result which provides an affirmative answer to this conjecture. The method of proof uses recent joint work with [[Dmitri Pavlov]] on the [geometric cobordism hypothesis](cobordism+hypothesis#ReferencesGeometricCobordisms).

\linebreak

* {#BerwickEvansMar23} [[Daniel Berwick-Evans]] (University of Illinois Urbana-Champaign)

  **How do field theories detect the torsion in topological modular forms?**

  cf.: [arXiv:2303.09138](https://arxiv.org/abs/2303.09138)

  video: [YT](https://www.youtube.com/watch?v=fw7yxFsDmjs)

  > Since the mid 1980s, there have been hints of a deep connection between [[2d CFT|2-dimensional]] [[quantum field theory|field theories]] and [[elliptic cohomology]]. This lead to [[What is an elliptic object?|Stolz and Teichner's conjectured geometric model]] for the universal [[elliptic cohomology]] [[Whitehead-generalized cohomology|theory]] of [[topological modular forms]] ([[TMF]]) in which [[cocycles]] are [[(2,1)-dimensional Euclidean field theory|2-dimensional supersymmetric field theories]]. Basic properties of these field theories lead to expected integrality and modularity properties, but the abundant [[torsion subgroup|torsion]] in [[TMF]] has always been mysterious. In this talk, I will describe deformation invariants of 2-dimensional field theories that realize certain torsion classes in TMF. This leads to a description of the generator of [[tmf#HomotopyGroups|$\pi_3(TMF) =\mathbb{Z}/24$]] in terms of the [[(2,1)-dimensional Euclidean field theory|supersymmetric sigma model]] with [[target space|target]] [[3-sphere|$S^3$]].

\linebreak

* {#SchweigertMar2023} [[Christoph Schweigert]] (Hamburg University)

  **String-net methods for CFT correlators**

  cf.: [arXiv:2302.01468](https://arxiv.org/abs/2302.01468)

  slides: [[Schweigert-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=JOF72-GXFYw)

  > Based on a [[string diagram|graphical calculus]] for [[pivotal category|pivotal]] [[bicategories]], we develop a [[string-net model|string-net construction]] of a [[modular functor]]. We show that a rigid separable Frobenius functor between strictly pivotal bicategories induces a [[linear map]] between the corresponding bicategorical string-net spaces that is compatible with the [[mapping class group]] [[group action|actions]] and with [[sewing constraint|sewing]]. This result implies that [[correlators]] of [[2d CFT|two-dimensional conformal field theories]] factorize over string-net spaces constructed from [[defect QFT|defect data]].

\linebreak

* {#BeliakovaMar2023} [[Anna Beliakova]] (University of Zurich):

  **On algebraisation of low-dimensional Topology**

  cf.: [arXiv:2205.11385](https://arxiv.org/abs/2205.11385)

  video: [YT](https://www.youtube.com/watch?v=7I5526YkI44)

  > [[cobordism category|Categories of $n$-cobordisms]]  (for $n=2$, $3$ and $4$) are among the most studied objects in [[low dimensional topology]]. For $n=2$ we know that $2Cob$ is a [[monoidal category]] [[free construction|freely generated]] by its [[commutative algebra|commutsative]] [[Frobenius algebra]] [[object]]: the [[circle]]. This result also classifies all [[TQFT]] functors on $2Cob$. In this talk I will present similar classification results for special categories of 3- and 4-[[cobordisms]]. They were obtained in [collaboration with Marco De Renzi](https://arxiv.org/abs/2205.11385) and are based on the [work of Bobtcheva and Piergallini](https://arxiv.org/abs/1108.2717). [[Frobenius algebra]] in these cases will be replaced by a braided [[Hopf algebra]].

  > I plan to finish by relating our results with the famous problem in [[combinatorial group theory]] — the [[Andrews–Curtis conjecture]].

\linebreak

* {#CollariMar2023} [[Carlo Collari]] (University of Pisa):

  **Weight systems which are quantum states**

  cf. [arXiv:2210.05399](https://ncatlab.org/schreiber/show/Fundamental+weight+systems+are+quantum+states#Collari2023)

  slides: [[Collari-WeightSystems.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=1De0T_8ojvs)

  > Roughly speaking, a [[weight system]] is a [[function]] from a space of [[chord diagrams]] to the [[complex numbers]]. Weight systems can be used to recover [[knot invariant|invariants]] for the relevant kind of knotted object (eg. [[knots]], [[links]], [[braids]] etc.) from the [[Kontsevich integral]]. The [[schreiber:Differential Cohomotopy implies intersecting brane observables|work of Sati and Schreiber]] highlighted the connection between ([[horizontal chord diagram|horizontal]]) [[chord diagrams]] and higher [[quantum observable|observables]] in quantum [[brane]] physics. This motivates the question: "which [[weight systems]] are [[state on a star-algebra|quantum states]]?" [[schreiber:Fundamental weight systems are quantum states|Corfield, Sati and Schreiber showed]] that all $\mathfrak{gl}(n)$ [[weight systems]] associated to the [[fundamental representation|defining representation]] are indeed [[state on a star-algebra|quantum states]]. In this talk I will present an extension of their result to more general weight systems.

  > The plan of the talk is the following; first, I will introduce the mathematical problem. Then, I will review the [[schreiber:Fundamental weight systems are quantum states|proof given by Corfield, Sati and Schreiber]] that $\mathfrak{gl}(n)$ weight systems associated to the defining representation are [[state on a star-algebra|quantum states]]. Finally, I will show how this result can be extended to weight systems associated to exterior and symmetric powers of the defining representation.

\linebreak

* {#BlumenhagenMar2023} [[Ralph Blumenhagen]] (Max-Planck-Institute for Physics, Munich):

  **Nullifying Cobordism in Quantum Gravity**

  cf.: [arXiv:2208.01656](https://arxiv.org/abs/2208.01656), [arXiv:2303.03423](https://arxiv.org/abs/2303.03423)

  slides: [[Blumenhagen-at-QFTAndCobordism2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=jLlE_jSH0lk)

  > In the [[swampland]] program one tries to delineate [[effective quantum field theory|effective theories]] consistent with [[quantum gravity]] from those which are not by so-called swampland conjecture. As a consequence of the absence of [[global symmetries]] in [[quantum gravity|QG]], [one such conjecture](swampland#SwamplandCobordismConjecture) is saying that the [[cobordism group]] has to vanish. In mathematics very often these groups do not vanish right away. Physics tells us that this can be ameliorated by either [[gauge symmetry|gauging]] or [[symmetry breaking|breaking]] of the corresponding global symmetries.

  > First, we show how the gauging fits into some known constraints in [[string theory]], the so-called [[tadpole cancellation]] conditions. Mathematically, this is reflecting a well known connection between certain [[topological K-theory|K-theory]] and [[cobordism groups]]. Second, we report on new results related to the breaking of a global symmetry via [[codimension]] one [[defect QFT|defects]]. In fact, going beyond topology a very similar mechanism arises for (for a long time puzzling) rolling solutions in string theory, giving rise to the notion of a dynamical cobordism conjecture.

\linebreak

* {#SatiMar2023} [[Hisham Sati]] (CQTS, NYU Abu Dhabi):

  **Cobordism in Quantum M-Theory 1: M/F-Theory as Mf-Theory**

  > In the quest for mathematical foundations of M-theory, the "[[schreiber:Hypothesis H|Hypothesis H]]" that [[flux quantization|fluxes are quantized]] in [[Cohomotopy theory]], implies that [[M-brane]] charges on flat [[spacetimes]] locally organize into equivariant [[homotopy groups of spheres]]. This leads generally to a correspondence between phenomena conjectured in [[M-theory]] and fundamental mathematical concepts/results in [[stable homotopy theory|stable homotopy]], [[generalized cohomology theory|generalized cohomology]] and [[Cobordism theory]] $M f$. (Based on [[schreiber:M/F-Theory as Mf-Theory|arxiv.org/abs/2103.01877]]).

\linebreak

* {#SchreiberMar2023} [[Urs Schreiber]]

  **Cobordism in Quantum M-Theory 2: Topological Quantum Gates in HoTT**

  cf.: [[schreiber:Topological Quantum Gates in Homotopy Type Theory|arXiv:2303.02382]]

  video: [YT](https://www.youtube.com/watch?v=pu5bpJ263X0)

  > [[schreiber:Anyonic defect branes in TED-K-theory|Recent results]] on [[defect branes]] in [[string theory|string]]/[[M-theory]] and on their [[AdS/CMT correspondence|holographically dual]] [[anyon|anyonic]] defects in [[condensed matter theory]] allow for the specification of realistic [[topological quantum computation|topological]] [[quantum gates]], operating by anyon defect [[braiding]] in [[topological order|topologically ordered]] [[quantum materials]]. This has a surprisingly slick formulation in [[parametrized homotopy theory|parameterized]] [[point-set topology]], which is so fundamental that it lends itself to [[software verification|certification]] in modern [[homotopy type theory|homotopically typed programming languages]], such as [[cubical Agda]]. (Based on [[schreiber:Anyonic topological order in TED K-theory|arxiv.org/abs/2303.02382]]).

\linebreak

### Apr 2023

* 27 Apr - 1 Mar 2023

  **[NYUAD Hackaton on Quantum Computing](https://nyuad.nyu.edu/en/events/2023/april/nyuad-hackathon-event.html)** 2023

  > on [[quantum computing]]/[[quantum programming]]

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\linebreak

### May 2023
 {#ConferencesMay2023}

{#QuantumConference2023} 22 - 26 May 2023

  **Quantum Information and Quantum Matter**

  > on [[quantum information]], [[quantum material|quantum matter]]

  [webpage](https://nyuad.nyu.edu/en/events/2023/may/quantum-information-quantum-matter.html)

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\linebreak

* {#AmicoMay2023} [[Luigi Amico]], (Technology Innovation Institute, Abu Dhabi):

  **Coherence of confined matter in lattice gauge theories at the mesoscopic scales**

  > [[atomtronics|Atomtronics]] is the emerging quantum technology of matter-wave circuits which coherently guide propagating ultra-cold atoms. The field benefits from the remarkable progress in micro optics, allowing to control the coherent matter with enhanced flexibility on the micron spatial scale. This way, both fundamental studies in quantum science and technological applications can be carried out. I will sketch recent progress in matter-wave circuitry and [[atomtronics]]-based quantum technology. In particular,  I will focus on a specific  scheme [[quantum simulation|simulating]] [[lattice gauge theories]] and analyze [[confinement|confined]] matter at the mesoscopic spatial scale.

\linebreak

* {#ByrnesMay2023} [[Tim Byrnes]] (NYU Shanghai):

  **Measurement based imaginary time evolution**

  cf. [arXiv:2210.06923](https://arxiv.org/abs/2210.06923)

\linebreak

* {#SchoellerMay2023} Herbert Schoeller (RWTH Aachen):

  **Supersymmetry protected topological states and realization of periodic Witten models in two dimensional second-order topological insulators**

  cf.: [arXiv:2212.01307](https://arxiv.org/abs/2212.01307)

  > For a generic two-dimensional [[topological insulator]] with band inversion and [[spin-orbit coupling]], we propose the generation of topological zero-energy [[bound states]] via the application of an in-plane Zeeman field breaking rotational invariance. The Zeeman field induces a surface gap and generates the topological states via a second-order mechanism generically at the surface positions where the normal component of the Zeeman field vanishes. Via the application of an additional half-integer [[Aharonov-Bohm effect|Aharonov-Bohm]] [[flux]] through a hole of the system, we show that the topological states are protected by supersymmetry. For smooth surfaces, we derive an effective surface Hamiltonian in the form of a periodic Witten model and propose how the surface bound states of the supersymmetric spectrum can be calculated via a trapping mechanism in effective surface potentials. We study the whole phase diagram of the model together with its stability and discuss the high tunability of the topological states.

\linebreak

* {#BouhonMay2023} [[Adrien Bouhon]] (Cambridge University):

  **Non-abelian and Euler multi-gap topologies in crystalline materials**

  on [braiding of band nodes in momentum space](braid+group+statistics#ReferencesAnyonicBraidingInMomentumSpace)

\linebreak

* [[Markus Müller]] (RWTH Aachen University and Forschungszentrum Jülich, Germany):

  **Fault-Tolerant Topological Quantum Computing: From Concepts to Experiments**

  > To date, the construction of scalable fault-tolerant [[quantum computers]] remains a fundamental scientific and technological challenge, due to the influence of unavoidable [[noise]]. In my talk, I will first introduce basic concepts of topological [[quantum error correction codes]], which allow one to protect quantum information during storage and processing. I will discuss recent theory work, perspectives and recent collaborative experimental breakthroughs towards fault-tolerant [[quantum error correction]] on various physical quantum computing platforms. This includes the first realisation of repeated high-performance quantum error-correction cycles on a topological surface code with [superconducting qubits](superconductivity#SuperconductingQBitsReferences) [1], and the first demonstration of a universal and fault-tolerant logical gate set with trapped ions [2]. Furthermore, I will present new fundamental connections between topological [[quantum error correction]] and classical statistical mechanics models, in the context of the correction of qubit loss [3,4] and the determination of fundamental error thresholds for circuit noise [5].

  > [1] S. Krinner et al., *Realizing repeated quantum error correction in a distance-three surface code*, [Nature 605, 669 (2022)](quantum+error+correction#MüllerWallraffEtAl22)

  > [2] L. Postler et al., Demonstration of fault-tolerant universal quantum gate operations, Nature 605, 675 (2022)

  > [3] D. Vodola, et al., Twins Percolation

  > [4] R. Stricker et al., Deterministic correction of qubit loss, Nature 585, 207 (2020)

  > [5] D. Vodola et al., Fundamental thresholds of realistic quantum error correction circuits from classical spin models, Quantum 6, 618 (2022)

\linebreak

* (...)

\linebreak

### Oct 2023

20 Oct 2023

**Workshop on Homotopy Theory and Applications**
 {#WorkshopOnHomotopyTheory2023}

\linebreak

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* {#KallelOct2023} [[Sadok Kallel]]:

  **The Homotopy Type of Graph Configuration Spaces**

  on [[configuration spaces of points]]

  slides: [[Kallel-GraphConfiguration.pdf:file]]

  video: [YT](https://youtu.be/eNdPBkjA-eQ)

* {#MyersOct2023} [[David Jaz Myers]]:

  **Homotopy Manifolds and Tangent Bundles in HoTT**

  on [[homotopy types]] of [[smooth manifolds]] in [[homotopy type theory]]

  video: [YT](https://youtu.be/LSMz8gQNfyk)

  cf. upcoming preprint

* {#MoserOct2023} [[Lyne Moser]]:

  **Model Structures for Double Categories**

  on [[model structures on DblCat]]

  video: [YT](https://youtu.be/8j1WvFesnQM)

  cf. [arXiv:2004.14233](https://arxiv.org/abs/2004.14233), [arXiv:2007.00588](https://arxiv.org/abs/2007.00588)

* {#CloughOct2023} [[Adrian Clough]]:

  **The Homotopy Theory of Differentiable Sheaves**

  on the [[homotopy theory]] of [[smooth infinity-groupoids|smooth $\infty$-groupoids]]

  video: [YT](https://youtu.be/5NrKo-fPk2A)

  cf. [arXiv:2309.01757](https://arxiv.org/abs/2309.01757)

* {#HuanOct2023} [[Zhen Huan]]:

  **2-Representations and 2-Vector Bundles**

  cf. [arXiv:2208.10042](https://arxiv.org/abs/2208.10042)

  on [[2-representations]] and [[2-vector bundles]]

* {#SchreiberOct2023} [[Urs Schreiber]]:

  **[[schreiber:Higher Topos Theory in Physics|Higher Topos Theory in Physics]]**

  on [[higher topos theory|higher]] [[topos theory]] in [[mathematical physics]]

  video: [YT](https://youtu.be/wNhoAiITJQs)

  cf.: [arXiv:2311.11026](https://arxiv.org/abs/2311.11026)

\linebreak

### Jan 2024
 {#Jan2024}

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**[[M-Theory and Mathematics]] 2024**

on January 15 - 17,  2024

at [[CQTS]] @ New York University, Abu Dhabi

* program: [[MTheoryAndMath2024-Program.pdf:file]]

* abstracts: [[MTheoryAndMath2024-Abstracts.pdf:file]]

* poster: [[MTheoryAndMath2024-Poster.pdf:file]]

**Speakers:**

* [[Luigi Alfonsi]]

* [[Chris Blair]]

* [[Mario Garcia-Fernandez]]

* [[Grigorios Giotopoulos]]

* [[Fei Han]]

* [[Yang-Hui He]]

* [[Olaf Hohm]]

* [[Chris Hull]]

* [[Neil Lambert]]

* [[Emanuel Malek]]

* [[Ruben Minasian]]

* [[Christian Saemann]]

* [[Hisham Sati]]

* [[Urs Schreiber]]

* [[Carlos Shahbazi]]

* [[Eric Sharpe]]

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[[Luigi Alfonsi|Alfonsi]]$\,$[[Grigorios Giotopoulos|Giotop.]] [[Emanuel Malek|Malek]] [[Christian Saemann|Saemann]] [[Ruben Minasian|Minasian]] [[Neil Lambert|Lambert]] [[Chris Hull|Hull]] [[Urs Schreiber|Schreiber]] [[Yang-Hui He|He]] [[Hisham Sati|Sati]] X [[Fei Han|Han]] [[Meng-Chwan Tan|Tan]] [[Vivek Kumar Singh|Singh]] [[Carlos Shahbazi|Shahbazi]] [[David Jaz Myers|Myers]] [[Olaf Hohm|Hohm]]

\linebreak

**Talks:**

* {#LambertMThMath2024} 15 Jan 2024

  [[Neil Lambert]]:

  **Non-Relativistic M2-Branes and AdS/CFT**

  slides: [[Lambert-NonRelM2BranesAndADSCFT.pdf:file]]

  cf.: [arXiv:2401.14955](https://arxiv.org/abs/2401.14955)

  > We discuss a peculiar limit of [[M2-branes]] that leads to a non-relativistic [[ABJM model|Chern-Simons-matter theory]] with an infinite dimensional spacetime [[symmetry group]] and whose dynamics leads to [[quantum mechanics]] on a [[Hitchin moduli space]]. We also discuss the corresponding limit in the [[AdS-CFT correspondence|gravitational dual]] which is described by an eleven-dimensional Membrane-Newton-Cartan theory about a [[background field|background]] with an [[anti de Sitter spacetime|$AdS_2$]] factor.

\linebreak

* {#ShahbaziMThMath2024} 15 Jan 2024

  [[Carlos Shahbazi]]:

  **The Differential Geometry and Topology of Four-
Dimensional Universal Supergravity**

  slides: [[Shahbazi-MTheoryAndMath2024.pdf:file]]

  cf.: [arXiv:2101.07236](pre-metric+electromagnetism#LazaroiuShahbazi23)

  > Using the [[sheaf cohomology|cohomology]] of the appropriate [[locally constant sheaf]] I will explain how to implement the [[Dirac charge quantization|Dirac-Schwinger-Zwanziger integrality condition]] on [[D=4 supergravity|four-dimensional]] [[classical field theory|classical]] ungauged [[supergravity]] and how to interpret it geometrically in order to obtain its [[U-duality|duality]]-covariant, [[gauge theory|gauge-theoretic]], [[differential geometry|differential-geometric]] global model. Using this construction, I will prove that [[D=4 supergravity|four-dimensional]] bosonic un[[gauged supergravity|gauged]] [[supergravity]] is completely determined by a choice of polarized Siegel bundle defined over the total space of a vertically [[Riemannian manifold|Riemannian]] [[submersion]] equipped with a complete [[Ehresmann connection]], showing that its gauge sector reduces to a polarized [[self-dual higher gauge theory|self-duality condition]] for connections on the underlying polarized Siegel bundle. Furthermore, I will explore the continuous and arithmetic [[U-duality]] groups of the theory, characterizing them through [[short exact sequences]] and realizing the latter through the [[automorphism group]] of the underlying Siegel bundle acting on its [[adjoint bundle]]. This elucidates the geometric origin of [[U-duality]] and justifies the miraculous existence of U-dualities by describing them as a [[gauge transformation]] of the appropriately defined [[principal bundle]].

\linebreak

* 15 Jan 2024

  [[Mario Garcia-Fernandez]]:

  **Gauge Theory for String Algebroids**

  cf.: [arXiv:arXiv:2004.11399](string+algebroid#GarciaFernandezRubioTipler)

  > In this talk I will explain a [[moment map]] construction for [[string algebroids]], a special type of [[Courant algebroids]] which arise as [[Atiyah algebroids]] of [[principal 2-bundle|higher principal bundles]]. The zero locus of our moment map is given by the solutions of the Calabi system, a coupled system of equations which provides a unifying framework for the classical Calabi problem and the Hull-Strominger system in [[heterotic string theory]]. Our main results are concerned with the geometry of the [[moduli space]] of solutions, and assume a technical condition which is fulfilled in examples. We prove that the [[moduli space]] carries a pseudo-Kähler metric with Kähler potential given by the [[dilaton]] functional, a topological formula for the metric, and an infinitesimal Donaldson-Uhlenbeck-Yau type theorem. Based on joint work with Rubio and Tipler in [arXiv:arXiv:2004.11399](string+algebroid#GarciaFernandezRubioTipler) (to appear in JDG) and ongoing joint work with Álvarez-Cónsul and Tellez.

\linebreak

* {#GiotopoulosMThMath2024} 15 Jan 2024

  [[Grigorios Giotopoulos]]:

  **Towards Non-Perturbative Lagrangian Field Theory via
the Topos of Smooth Sets**

  cf.: [arXiv:2312.16301](smooth+set#GiotopoulosSati23)

  > Any notion of [[non-perturbative field theory|non-pertubative]] ([[prequantum geometry|pre]])-[[quantization]] of [[classical field theories]], as in particular expected in [[M-theory|M-theoretic]] contexts, presupposes a [[convenient category of topological spaces|convenient category]] within which non-pertubative classical field theory may be rigorously formalised. In this talk, I will describe [[smooth sets]] as a [[category]] of [[generalized smooth spaces]], completely determined by "how they may be smoothly probed by finite dimensional [[smooth manifold|manifolds]]". Formally, this is the "[[topos]] [[category of sheaves|of sheaves]] over the [[site]] of [[Cartesian spaces]]". I will then explain how the [[variational calculus|variational algorithm]] of ([[bosonic field|bosonic]]) [[classical field theory]] and the space of [[on-shell]] [[field (physics)|fields]] naturally take place in [[smooth sets]], along with many more field theoretic concepts. Time permitting, I will indicate how the setting naturally generalizes to include the description of [[synthetic differential geometry|infinitesimal]] (pertubative) structure, [[fermionic fields]], and ([[gauge field|gauge]]) fields with [[internal symmetries]].

\linebreak

* {#AlfonsiMThMath2024} 15 Jan 2024

  [[Luigi Alfonsi]]:

  **Towards Non-Perturbative BV-Theory via Derived
Geometry and the Puzzle of Quantisation**

  cf.: [arXiv:arXiv:2307.15106](BV-BRST+formalism#AlfonsiYoung23)

  > In this talk I will introduce and discuss a global geometric framework which allows one to encode a natural [[non-perturbative field theory|non-perturbative]] generalisation of classical [[BV-formalism|Batalin–Vilkovisky(BV-)theory]]. First, I will set the stage by briefly describing the current state of the art of [[perturbative quantum field theory|perturbative]] [[BV-theory]]. Then, I will introduce a concrete model of [derived differential geometry]], whose geometric objects are [[formal geometry|formal]] [[derived geometry|derived]] [[smooth stacks]] (i.e. [[stacks]] on formal [[derived smooth manifolds]]), and which is obtained by applying [Töen-Vezzosi's homotopical algebraic geometry](derived+algebraic+geometry#ToenVezzosi04) to the theory of [[derived manifolds]] of [Spivak](derived+smooth+manifold#Spivak08) and [Carchedi-Steffens](derived+smooth+manifold#CarchediSteffens19). I will explain how derived differential geometry is able to capture non-perturbative classical BV-theory by means of examples: [[scalar field theory]] and [[Yang-Mills theory]]. Finally, I will discuss some open questions, most importantly on [[quantisation]] and on applications to global aspects of [[M-theory]].

\linebreak

* {#SharpeMThMath2024} 15 Jan 2024

  [[Eric Sharpe]]:

  **Decomposition of 2D Pure Yang-Mills and the Gross-
Taylor String Theory**

  slides: [[Sharpe-MTheoryMath2024.pdf:file]]

  cf.: [arXiv:2307.08729](https://arxiv.org/abs/2307.08729)

  > In this talk, we will attempt to reconcile two different results on [[D=2 Yang-Mills theory|two-dimensional pure Yang-Mills theory]]. Specifically, we will discuss how the fact that [[D=2 Yang-Mills theory|2d pure Yang-Mills]] is equivalent to a disjoint union of theories, is related to the Gross-Taylor description of 2d pure Yang-Mills as the [[target space|target-space]] field theory of a [[string theory]]. The Gross-Taylor picture can be understood by first rewriting the Yang-Mills partition function (in a [[large N limit|large $N$ limit]]) as a sum of [[correlation functions]] in [[Dijkgraaf-Witten theories]] for the [[symmetric group]] $S_n$, and then interpreting those Dijkgraaf-Witten correlation functions in terms of [[branched covers]], which leads to the string theory description. We first observe that the decomposition of the pure Yang-Mills aligns perfectly with the decomposition of $S_n$ Dijkgraaf-Witten theory, and then discuss decomposition and the branched covers interpretation. We encounter two puzzles, and to solve them, propose that the Gross-Taylor string theory has a [[higher form symmetry|higher-form symmetry]].

\linebreak

* {#MinasianMThMath2024} 16 Jan 2024

  [[Ruben Minasian]]:

  **Constraining and Un-constraining Supergravities**

  slides: [[Minasian-MTheoryAndMath2024.pdf:file]]

  > I will review various aspects and somewhat surprising consequences of cancellation of (different types of) [[anomalies]] in [[supergravity]] theories in [[D=8 supergravity|eight]] and [[D=6 supergravity|six]] dimensions. I will also discuss appearance and importance of exotic (singular, non-spin, non-orientable) [[background field|backgrounds]].

\linebreak

* {#MalekMThMath2024} 16 Jan 2024

  [[Emanuel Malek]]:

  **Kaluza-Klein Spectrometry for String Theory
Compactifications**

  cf.: [arXiv:2212.01135](exceptional+field+theory#DuboeufMalekSamtleben23)

  > I will present a powerful new method that for the first time allows us to compute the [[Kaluza-Klein theory|Kaluza-Klein]] spectrum of a large class of [[string theory]] [[KK-compactification|compactifications]], including those arising in maximal [[gauged supergravities]] and beyond. This includes geometries with little to no remaining ([[supersymmetry|super]]-)[[symmetries]], completely inaccessible by previous methods. I will show how these insights can be used to [[holographic principle|holographically]] compute the anomalous dimensions of protected and unprotected operators in [[non-perturbative quantum field theory|strongly-coupled]] [[CFTs]], as well as to study global properties of their conformal manifolds. I will also show how the method can be used to determine the perturbative stability of non supersymmetric [[anti-de Sitter spacetime|AdS]] [[string theory vacuum|vacua]]. We will see the importance of higher Kaluza-Klein modes to the physics of string compactifications, e.g. in realising the compactness of moduli spaces, restoring [[supersymmetry]] that is lost in a consistent truncation, and in destabilising vacua that appear to stable in lower-dimensional supergravities.

\linebreak

* {#HanMThMath2024} 16 Jan 2024

  [[Fei Han]]:

  **Cubic Forms, Anomaly Cancellation and Modularity**

  cf.: [arXiv:2005.02344](https://arxiv.org/abs/2005.02344)

  > [Freed and Hopkins developed](D=11+N=1+supergravity#FreedHopkins21) an algebraic theory of cubic forms, which is an analogy to the theory of [[quadratic forms]] in topology. They are motivated by the Witten-Freed-Hopkins anomaly cancellation formula in [[M-theory]], which equals a cubic form arising from an [[E8|$E_8$]] [[principal bundle|bundle]] over a 12 dimensional [[spin manifold]] to the [[index of a Dirac operator|indices]] of twisted [[Dirac operators]] on the manifold. In this talk, we will first review the Witten-Freed-Hopkins anomaly cancellation formula and the algebraic theory of cubic forms, and then show that the cubic forms as well as the anomaly cancellation formula can be naturally derived from [[modular forms]] that we construct inspired by the [[Witten genus]] and the basic representation of [[affine Lie algebra|affine]] [[E8|$\mathfrak{e}_8$]]. Following this approach, we obtain new cubic forms and anomaly cancellation formulas on non-spin manifolds and thus provide a unified way to obtain anomaly cancellation formulas of this type. This is based on our [joint work](D=D11+N=1+supergravity#HanHuangLiuZhang20) with Prof. [[Ruizhi Huang]], Prof. [[Kefeng Liu]] and Prof. [[Weiping Zhang]].

\linebreak

* {#TanMThMath2024} 16 Jan 2024

  [[Meng-Chwan Tan]]:

  **Topological-Holomorphic $\mathcal{N}=4$ Gauge Theory: From Langlands Duality of Holomorphic Invariants to Mirror Symmetry of Quasi-Topological Strings**

  slides: [[Tan-MTheoryAndMath2024.pdf:file]]

  cf.: [arXiv:2305.15965](https://arxiv.org/abs/2305.15965)

  > We perform a topological-holomorphic [[topological twist|twist]] of [[D=4 N=4 SYM|$\mathcal{N}=4$]] [[super Yang-Mills theory|supersymmetric gauge theory]] on a [[4-manifold|four-manifold]] of the form $M^4 = \Sigma_1 \times \Sigma_2$, and unravel the mathematical implications of its physics. In particular, we consider the cohomology of different linear combinations of the resulting scalar supercharges under [[S-duality]], whence we would be able to derive novel topological and holomorphic invariants of $M^4$ and their [[geometric Langlands duality|Langlands duals]]. As the twisted theory can be topological along $\Sigma_1$ such that we can [[KK-reduction|dimensionally reduce]] it to 2d, via the [[effective field theory|effective]] [[sigma-model]] on $\mathbb{C}_2$, we can also relate these 4d invariants and their Langlands duals to the [[mirror symmetry]] of [[Higgs bundles]] and that of quasi-topological strings described by the [[sheaf]] of [[chiral differential operators]].

\linebreak

* {#HohmMThMath2024} 16 Jan 2024

  [[Olaf Hohm]]:

  **Double Copy, Double Field Theory & Homotopy
Algebras**

  > The [[double copy]] denotes a technology to relate the [[scattering amplitudes]] of [[Yang-Mills theory]] to those of [[gravity]]. While enormously successful at the level of [[scattering amplitudes]], until recently there was no first-principle understanding of how to derive such relations. Such an understanding would be needed in order to describe, for instance, a double copy of classical solutions. I present an approach based on [[homotopy algebras]] such as [[L-infinity algebras|L-infinity algebras]] that allows one to provide such a first-principle derivation, at least to some finite order in [[perturbation theory]]. To this end I review how to formulate [[Yang-Mills theory]] as an [[L-infinity algebra]], how to "strip off" [[color charge|color]] to obtain a different kind of homotopy algebra and, finally, how to combine two copies of these exotic algebras to obtain the L-infinity algebra of gravity in the form of [[double field theory]].

\linebreak

* {#SaemannMThMath2024} 16 Jan 2024

  [[Christian Saemann]]:

  **Atiyah Algebroids for Higher and Groupoid Gauge
Theories**

  slides: [[Saemann-AtiyahAlgebroids.pdf:file]]

  > We present an [[Atiyah Lie algebroid|Atiyah algebroid]] picture for [[higher gauge theory|higher]] and groupoid [[gauge theories]]. Common to both is the fact that straightforward definitions of [[curvatures]] are only suitable for partially [[flat bundle|flat]] cases. Instead, one has to adjust the underlying [[cocycle]] relations, leading to new curvatures and gauge transformations. The Atiyah algebroid picture I sketch provides a good idea about the origin of [[adjusted Weil algebra|adjustments]] and why they are required even in the relative conventional case of groupoid gauge theories.

\linebreak

* {#HullMThMath2024} 17 Jan 2024

  [[Chris Hull]]:

  **Self-Dual $p$-Form Gauge Fields and the Topology of the
Graviton**

  slides: [[Hull-MTheoryAndMath2024.pdf:file]]

  cf.: [arXiv:2307.04748](self-dual+higher+gauge+theory#Hull23)

  > [Sen's action](self-dual+higher+gauge+theory#Sen20) for a [[higher gauge field|$p$-form gauge field]] with [[self-dual higher gauge theory|self-dual]] [[field strength]] coupled to a [[spacetime]] [[Riemannian metric|metric]] involves an explicit [[Minkowski metric]] and the presence of this raises questions as to whether the action is [[coordinate]] independent and whether it can be used on a general spacetime [[manifold]]. A natural generalisation of [Sen's action](self-dual+higher+gauge+theory#Sen20) is presented in which the Minkowski metric is replaced by a second metric on spacetime. The theory is covariant and can be formulated on any spacetime. The theory describes a physical sector, consisting of the [[self-dual higher gauge theory|chiral $p$-form gauge field]] coupled to the dynamical metric $g$, plus a shadow sector consisting of a second chiral $p$-form and the second metric. The resulting theory is covariant and can be formulated on any spacetime. A spacetime with two metrics has some interesting geometry and some of this is explored here and used in the construction of the interactions. The action has two [[diffeomorphism]]-like symmetries, one acting only on the physical sector and one acting only on the shadow sector, with the spacetime diffeomorphism symmetry arising as the diagonal subgroup.

\linebreak

* {#HeMThMath2024} 17 Jan 2024

  [[Yang-Hui He]]:

  **The AI Mathematician**

  > We summarize how [[artificial intelligence|AI]] can approach mathematics in three ways: [[proof assistant|theorem-proving]], [[conjecture]] formulation, and [[natural language|language]] processing. Inspired by initial experiments in [[geometry]] and [[string theory]], we present a number of recent experiments on how various standard [[machine learning|machine-learning]] [[algorithms]] can help with pattern detection across disciplines ranging from [[algebraic geometry]] to [[representation theory]], to [[combinatorics]], and to [[number theory]].

\linebreak

* 17 Jan 2024

  [[Chris Blair]]:

  **Geometry and Dualities of Decoupling Limits in String
Theory and M-Theory**

  cf.: [arXiv:2311.10564](https://arxiv.org/abs/2311.10564)

  > Our understanding of [[M-theory]] is based on a [[duality in string theory|duality web]] connecting different limits of the theory. I'll discuss the extension of this duality web to a wide variety of decoupling limits related by duality to the null reduction of M-theory (and hence to the proposal that M-theory can be described by [[BFSS matrix model|Matrix theory]]). From a modern perspective, these limits involve non-[[relativistic field theory|relativistic]] geometries, leading to new variants of [[supergravity]] in [[D=11 supergravity|11-]] and [[D=10 supergravity|10-dimensions]]. I'll discuss how to systematically explore these corners of M-theory, following the roadmap of [arxiv.org/abs/2311.10564](https://arxiv.org/abs/2311.10564).

\linebreak

* {#SatiMThMath2024} 17 Jan 2024

  [[Hisham Sati]]:

  **M-Theory and Hypothesis H**

  > I will survey the ([[cohomotopy|co]])[[homotopy theory|homotopical]] perspective on the [[field (physics)|fields]] and [[branes]] in [[M-theory]], showcasing several recent developments. This talk highlights the [[classical field theory|classical]]/[[prequantum field theory|prequantum]] aspects, while the [talk by Urs Schreiber](#Schreiber2024) will highlight the [[quantum physics|quantum]] aspects.

\linebreak

* {#SchreiberMThMath2024} 17 Jan 2024

  [[Urs Schreiber]]:

  **[[schreiber:Introduction to Hypothesis H|Introduction to Quantum Hypothesis H]]**

  > A famous [[hypothesis]] in [[string theory]] [[D-brane charge quantization in K-theory|says]] that the [[RR-fields]] in [[10d supergravity]] are subject to "[[flux quantization]]" in [[topological K-theory|topological K-cohomology]] theory. From a modernized point of view of [[rational homotopy theory]], analogous reasoning applies to the [[supergravity C-field|C-field]] in [[11d supergravity]] and suggests that its flux should be quantized in the "[[Cohomotopy|unstable CoHomotopy]]" [[cohomology theory]] of [Borsuk](cohomotopy#Borsuk36), [Pontrjagin](cohomotopy#Pontryagin38a) and [Spanier](#Spanier49). I'll survey this "[[schreiber:Hypothesis H]]" with focus on its implications for [[quantum observables]] on [[intersecting branes]]. This is joint work with [[Hisham Sati]]. Notes are available at: *[[schreiber:Hypothesis H|ncatlab.org/schreiber/show/Introduction+to+Hypothesis+H]]*.

\linebreak

### Apr 2024
 {#Apr2024}

19-21 April 2024

{#RunningHoTT2024} **Homotopy Type Theory and Computing -- Classical and Quantum**

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    "width": 110,
    "unit": "px",
    "margin": {
        "top": -35,
        "bottom": 20,
        "right": 70,
        "left": 40
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> The aim of this conference is to discuss [[homotopy type theory|Homotopy Type Theory Theory]] (`HoTT`) as a substrate for [[computing]] and [[software verification|verification]] in software development, in [[synthetic homotopy theory]], and possibly in application to ([[topological quantum computing|topological]]) [[quantum computing]]/[[quantum simulation|simulation]].

> Some talks will focus on recent progress on the general issue of running `HoTT` programs, in view of the [[univalence axiom]]: such as via "[[cubical type theory|cubical TT]]" or the more recent "[[higher observational type theory|higher observational TT]]". Other talks will focus on design patterns for practical ([[quantum programming language|quantum]]) [[programming language|programming]] and [[software verification|certification languages]], notably via [[modal types]] and [[monadic effects]] (in [[modal homotopy type theory|modal extensions of HoTT]]).

> In this vein, our local speakers will present a point of contact between modal `HoTT` and Quantum: the recently developed "[[linear homotopy type theory|Linear HoTT]]" (`LHoTT`) that equips classical `HoTT` with [[dependent linear type theory|dependent]] "[[linear type theory|linear]]" types which may be thought of as quantum [[data types]]. The `LHoTT` approach to quantum programming interprets a significant [[fragment]] of the [[Proto-Quipper]]-language, now with [[identity types]] enabling full [[software verification|verification]].

> The conference is to bring this theoretical progress into contact with efforts to use (`L`)`HoTT` and related languages like [[Proto-Quipper]] for actual ([[quantum computing|quantum]]) [[computing]], [[quantum simulation|simulation]] and [[software verification|verification]].

{#RunningHoTTSpeakers} **Speakers:**

* external:

  * [[Thorsten Altenkirch]]

  * [[Carlo Angiuli]]

  * [[Ulrik Buchholtz]]

  * [[Ugo Dal Lago]]

  * [[Eric Finster]]

  * [[Daniel Gratzer]]

  * [[András Kovács]]

  * [[Thomas Lamiaux]]

  * [[Axel Ljungström]]

  * [[Dongho Lee]]

  * [[Anders Mörtberg]]

  * [[Reed Mullanix]]

  * [[Jennifer Paykin]] (tbc)

  * [[Robert Rand]]

  * [[Jon Sterling]] (tbc)

  * [[David Wärn]]

* local:

  * [[David Jaz Myers]]

  * [[Mitchell Riley]]

  * [[Urs Schreiber]]

\linebreak

### May 2024

* 27 May - 31 May 2024

  **Quantum Information and Quantum Matter**

\linebreak

***

\linebreak

## Quantum Colloquium
 {#CQTSColloquium}

Weekly colloquium, broadly on [[quantum systems]], with focus on [[quantum computation]] and specifically on [[topological quantum computation]] and [[dependent type theory|dependently typed]] [[quantum programming languages]].

\linebreak

### May 2022

* [[Urs Schreiber]] on joint work with [[Hisham Sati]]:

  **[[schreiber:New Foundations for TDA -- Cohomotopy|New Foundations for Topological Data Analysis -- The Power of Cohomotopy]]**
  {#CQTSColloquiumCohomotopyFoundationsForTDA}

  \linebreak

  > The aim of *[[topological data analysis]]* (TDA) is to provide qualitative analysis of large data/parameter sets in a way which is *robust* against uncertainties and noise. This is accomplished using tools and theorems from the mathematical field of *[[algebraic topology]]*. While a tool called *[[persistent homology]]* has become the signature method of TDA, it tends to produce answers that are either hard to interpret (persistent [[cycles]]) or impossible to compute ([[well groups]]). Both problems are solved by a variant method $[$[FK17](persistent+cohomotopy#FranekKrcal17)$]$ which we may call *[[persistent cohomotopy]]*: A first result shows $[$[FKW18](persistent+cohomotopy#FranekKrcalWagner18)$]$ that this new method provides computable answers to the concrete question of detecting whether there exist data+parameters that meet a prescribed target indicator precisely, even in the presence of uncertainty and noise. More generally, efficient data analysis will require further refining [[persistent cohomotopy]] to [[equivariant cohomotopy]] and/or [[twisted cohomotopy]] $[$[[schreiber:Proper Orbifold Cohomology|SS20]]$]$. Curiously, these flavors of [[cohomotopy theory]] have [[Hypothesis H|profound relations]] to formal [[high energy physics]] and [[topological phase of matter|quantum materials]], connecting to which might help to further enhance the power of [[topological data analysis]].

\linebreak

### Sep 2022
 {#ColloquiumSep22}

\linebreak

* {#RileySep2022} 13 Sep 2022
  {#InitialResearcherMeeting-Riley}

  [[Mitchell Riley]] (NYU Abu Dhabi, [[CQTS]]):

  **Dependent Type Theories à la Carte**

  slides: [[CQTS-InitialResearcherMeeting-Riley-220913.pdf:file]]

  > on realizing [[linear homotopy type theory]]

\linebreak

* 14 Sep 2022
  {#InitialResearcherMeeting-Valera}

  [[Sachin Valera]] (NYU Abu Dhabi, [[CQTS]]):

  **A Quick Introduction to the Algebraic Theory of Anyons**

  slides: [[CQTS-InitialResearcherMeeting-Valera-220914.pdf:file]]

  > on [[anyon]] [[braid representation|braiding]] described by [[braided fusion categories]]

\linebreak

* 14 Sep 2022
  {#InitialResearcherMeeting-Schreiber}

  [[Urs Schreiber]] (NYU Abu Dhabi, [[CQTS]]):

  **Initial Researchers' Meeting -- Motivation, Strategy & Technology**

  slides: [[CQTS-InitialResearcherMeeting-Schreiber-220914.pdf:file]]

  > outline of a research program on [[schreiber:Topological Quantum Programming in TED-K]]

\linebreak

### Oct 2022
 {#ColloquiumOct22}

\linebreak

* 11 Oct 2022
  {#ByrnesOct2022}

  [[Tim Byrnes]] (NYU Shanghai, CQTS):

  **Topological quantum states for quantum computing and metrology**

  video: [rec](https://zoom.us/rec/play/C9FIF3w8M7p-sLNwtoTgywtsVY4F0c3ta-_dVYz71dLtqlAY1lUN_eYeeDjSrGFRZOIXrpufLlCCRUFj.UVvwJke1wgatH3ld?continueMode=true&iet=zsBuHUCJzvE3H2PaTuMGttQDBizWU5azmHiGOumYdCw.AG.xAZVLsivejisWxE0NsdP_T2V_IwMdelb0TE50GXWfwmrrG_hrmggbEioQbR0UNcAN3cDd02RmPjuNw8cBJddTCpvkIs39kErHpcQ9dpL68jEAPo.oPVriiO1MtUW5qCjcj-_gQ.gVeUtka3H4pKyvKW&_x_zm_rtaid=XdmVwP1bTcqHQXfyCJBkGQ.1667379052963.a3fc19b1a88d43cc4ce525059f7ce542&_x_zm_rhtaid=807)

  * Part I -- *Quantum teleportation of Majorana Zero Modes*

    slides: [[Byrnes-TopologicalQuantumStates.pdf:file]]

    > on [Phys. Rev. Lett. 126, 090502 (2021)](https://arxiv.org/abs/2009.07590)

  * Part II -- *Quantum Hall effect in Bose-Einstein condensates*

    slides: [[Byrnes-QHEinBEC.pdf:file]]

    > on [Phys. Rev. A 92.023629 (2015)](https://doi.org/10.1103/PhysRevA.92.023629) and [Phys. Rev. B 99, 184427 (2019)](https://arxiv.org/abs/1905.01459)

\linebreak

### Nov 2022

\linebreak

* 07 Nov 2022
  {#PachosNov2022}

  [[Jiannis Pachos]] (Leeds University, UK):

  **Non-abelian topological Berry-phases**

  video: [rec](https://zoom.us/rec/play/FZOBvACSJsDzpqZ0WIf4WItlhF08IxP-vrgrRlfqsWqHFm8LFiiy5JD_7kTu5d1-WldA0oxXXCgjlbAg.S-7IQQf-XfhxNIbG?continueMode=true&iet=wHgMaPo0jUhLbgeLcRNNRn4t5tDEUui0GTZy7IskgfM.AG.2korr3jfgIJd-6R5zSQmb3fYA-lyqwuLti8O9KDQ0vDH8BJ2-bMcnQ1yboWDw8reV-2SKgLjwd0sVdHZWJR43y1ixw0PN4rGqDzSb3jdnroRh3nsq2fYp2s4b7Iavne-LwST3jI59_Y.gBff8xUXVV4VPqWf5kNIpg.gASLSIaf0KVBzA1A&_x_zm_rtaid=MnFZqJMnRzKokesOCUS66w.1667975314563.2bcd3ca7ce0a0ad02b775305bfa3c96f&_x_zm_rhtaid=473)

  > Combining physics, mathematics and computer science, [[topological quantum computation|topological quantum information]] [[1]](#PachosRefNov22) is a rapidly expanding field of research focused on the exploration of quantum evolutions that are resilient to errors. In this talk I will present a variety of different topics starting from introducing [[anyon|anyonic models]], [[topological phases of matter]], [[Majorana fermions]], characterising [[knot invariants]], their [[quantum simulation]] with [[anyons]] and finally the possible realisation of anyons in the laboratory.

  > $\,$

  > {#PachosRefNov22} [1] [[Jiannis K. Pachos]], *Introduction to Topological Quantum Computation*, Cambridge University Press (2012) $[$[doi:10.1017/CBO9780511792908]( https://doi.org/10.1017/CBO9780511792908)$]$

\linebreak

* 14 Nov 2022
  {#ValeraNov2022}

  [[Sachin Valera]] (NYU Abi Dhabi, [[CQTS]]):

  **A Quick Introduction to the Algebraic Theory of Anyons** (Part II)

  slides: [[CQTS-InitialResearcherMeeting-Valera-220914.pdf:file]]

  > on [[anyon]] [[braid representation|braiding]] described by [[braided fusion categories]]

\linebreak

* {#KentNov22} 21 Nov 2022

  [[Andrew Kent]] (Center for Quantum Phenomena, NYU)

  **A new spin on magnetism with applications in information processing**

  slides: [[Kent-CQTS-Nov2022.pdf:file]]

  video: [rec](https://drive.google.com/file/d/1LTz2y6KrJytps94rlS6o0BET6rmzPFU_/view), [YT](https://www.youtube.com/watch?v=uyKKNAmKRcs)

  > Recent advances in magnetism research are likely to have an important impact on electronics and information processing. These advances use the electron magnetic moment (spin) to transmit, write and store information. They enable new devices that operate at high speed with very low energy consumption. The information is stored in the orientation of electron magnetic moments in magnetic materials and can persist without power; energy is only needed to write and read the information. Important physics concepts include the interconversion of electrical (charge) currents into spin currents, the efficiency of the interconversion, controlling the currents, spin polarization direction, and the associated spin torques on magnetic order. [Magnetic skyrmions](skyrmion#ReferencesInSolidStatePhysics) are also of interest both because of their stability --- they are topologically protected objects --- and because their nucleation and motion can be controlled using spin currents. In this talk I will highlight the new physics concepts that have enabled these advances and discuss some of their applications in information processing.

> cf.: J. Appl. Phys. **130** (2021) [[doi:10.1063/5.0046950](https://doi.org/10.1063/5.0046950)]

\linebreak

* {#EqubalNov22} 28 Nov 2022

  [[Asif Equbal]] (NYU Abu Dhabi, CQTS)

  **Molecular spin qubits for future quantum technology**

  slides: [[Equbal-CQTS-Nov2022.pdf:file]]

  video: [rec](https://nyu.zoom.us/rec/play/YTjIGL-Bevb1H44UuL-ZimXdxph5cffddWpP3H4ZsuRT2xu3OrnTbC0NZLsKedUGwS68DJ8onVFPAETb.rreoi7Wt6uXFyaYN?continueMode=true&_x_zm_rtaid=e0VPIMlfT9KlVd_wiaOq6A.1669794985784.11f8cd37091ebf6bdd2a878668e26cd6&_x_zm_rhtaid=404), [YT](https://www.youtube.com/watch?v=wceg7E1p5Kg)

  cf.: *[spin resonance qbits](nuclear+magnetic+resonance#SpinResonanceQBitsReferences)*

  > [[spin|Spins]] are a purely [[quantum mechanics|quantum mechanical]] phenomenon and have been proposed as one of the several candidates for [[qubits]] in [[quantum information theory|quantum information science]]. [[quantum computer|Quantum computers]] based on [[spin]] [[qubits]] were first [proposed by DiVincenzo](quantum+computation#DiVincenzo00), who established five necessary criteria for building a [[quantum computer]]. The technology to control the [[quantum states]] of [[nuclear magnetic resonance|nuclear]] and [[electron]] [[spins]] and the theory of spin-spin and spin-[[magnetic field]] [[interactions]] are well developed, but a quantum computer based on spin qubits has not yet been realized. Why is this?

  > In this talk, I will discuss the challenges in developing spin qubits that meet [DiVincenzo's criteria](quantum+computation#DiVincenzo00) for [[quantum computers]]. First, I will explain in a pedagogical way how to manipulate spins in an external [[magnetic field]] that form the building block of [[quantum logic gates]]. I will then provide some insight into my own recent research on the development of optically polarized molecular spin qubits in solids.

\linebreak

### Dec 2022

\linebreak

* {#AolitaDec2022} 12 Dec 2022

  [[Leandro Aolita]]

  **Quantum Algorithms, from noisy intermediate scale devices through the early fault-tolerant era**

  video: [rec](https://nyu.zoom.us/rec/share/ASWX0PDAIgB_fn-KLdF9t-lg2M62LAmTUJIvHKuTiK7K1XjRmdQ7GFmnEzfHlfxf.DQSy2riBLwIEgZvp?startTime=1670850106000), [YT](https://www.youtube.com/watch?v=YljNgMWd4W8)

  > Reaching long-term maturity in [[quantum computation]] science and technology relies on the field delivering practically useful application in a short term. In this colloquium, I will discuss ideas for the noisy intermediate scale (NISQ) and early [[quantum error correction|fault-tolerant]] eras. I will divide my talk into two parts. In the first part, I will make a brief non-technical introduction to the field, its relevance to the UAE, and the main lines of research of the [Quantum Algorithms](https://www.tii.ae/quantum/our-research/quantum-algorithms) division at [QRC](https://www.tii.ae/quantum)-[TII](https://www.tii.ae/).

  > In the second one, I will try to convey some level of technical detail about our work. In particular, I will first present a hybrid classical-quantum algorithm to simulate high-connectivity quantum circuits from low-connectivity ones. This provides a versatile toolbox for both error-mitigation and circuit boosts useful for NISQ computations. Then, I will move on to algorithms for the forthcoming quantum hardware of the early fault-tolerant era: I will present a new generation of high-precision algorithms for [simulating quantum imaginary-time evolution](repeat-until-success+computing#AolitaEtAl21) (QITE) that are significantly simpler than current schemes based on quantum amplitude amplification (QAA). QITE is central not only to ground-state optimisations but also to partition-function estimation and Gibbs-state sampling, with a plethora of computational applications.

\linebreak

### Jan 2023

* {#SinghJan2023} 30 Jan 2023

  [[Vivek Singh]] ([[CQTS]] @ NYU Abu Dhabi)

  **Chern-Simons theory, Knot polynomials & Quivers**

  slides: [[Singh-CQTS-230130.pdf:file]]

  video: [rec](https://nyu.zoom.us/rec/play/muLFC8rM9dqGp9OALgnVHx7zlkOkMGNA0OT4_OLowBMr1DfH2FL0ZHPC1JcBjxzMc1dwWYWivPkxCkNc.iXT4MQtD8XwT_av3?continueMode=true&_x_zm_rtaid=PE1QubLLRRqlcRKK1X-mgA.1675146681717.847782ca2b7ab36562f3b33ce99ec7dd&_x_zm_rhtaid=941), [YT](https://www.youtube.com/watch?v=kflh-6KEjh8)

  cf. [arXiv:2103.10228](https://arxiv.org/abs/2103.10228)

  >  First, I will give a brief introduction to [[knot theory]] and its connection to [[Chern-Simons theory|Chern-Simons]] [[quantization of 3d Chern-Simons theory|quantum field theory]]. Then I discuss the method of obtaining polynomial invariants and limitations towards tackling classification of knots. In particular, we will highlight our new results on weaving knots and review the recent developments on Knot-Quiver correspondence.

\linebreak

### Feb 2023

* 13 Feb 2023

  Kazuki Ikeda ([Co-design Center for Quantum Advantage](https://www.bnl.gov/quantumcenter/), Stony Brook University, USA)

  **Demonstration of Quantum Energy Teleportation by Superconducting Quantum Processors and Implications for Communications and High Energy Physics**

  > Quantum energy teleportation is a theoretical concept in [[quantum physics]] that describes the transfer of [[energy]] from one location to another without the need for a physical medium to carry it. This is made possible by means of universal properties of [[quantum entanglement]] and measurement of quantum states. The role of QET in physics and information engineering is largely unexplored, as the theory has not received much attention for long time since it was proposed about 15 years ago. To validate it on a real quantum processor, my research has tested the energy teleportation protocol in its most visible form for the first time on IBM's superconducting quantum computer. In my colloquium talk, I will explain the historical background of quantum energy teleportation, quantum circuits and quantum operations. Moreover I will present a concrete setup for a long-distance and large-scale quantum energy teleportation with real [[quantum networks]].

  > In addition, I will present the results of [[quantum simulations]] with relativistic field theory as a study based on the high-energy physics perspective and the [[symmetry protected topological phase|symmetry-protected topological (SPT) phase of matter]] of quantum energy teleportation. The models will describe include the two dimensional QED (the massive Thirring model), the AKLT model, the [[Haldane model]], and the Kitaev model. Those results show that the phase diagrams of the field theory and SPT phase are closely related to energy teleportation.

  > In summary my talk will provide a novel suggestion that quantum energy teleportation paves a new pathway to a link between quantum communication on real [[quantum network]], phase diagram of quantum many-body system, and quantum computation.

\linebreak

* {#MurrayFeb2023} 20 Feb 2023

  [[Zachary Murray]]

  **Constructive Real Numbers in the Agda Proof Assistant**

  cf. [arXiv:2205.08354](https://arxiv.org/abs/2205.08354)

  video: [rec](https://nyu.zoom.us/rec/play/jZpU2ntT2u61_tnNIQZgJOHLvrc8w6t-7IjsWf6_TOuOVCgJoLwZtGg_33ZkUqIzmK9LZl7BRiElaZLq.tsHNOk7epHU9RWYE?continueMode=true), [YT](https://www.youtube.com/watch?v=7Q_sjfyPJqU)

  > [[proof assistant|Proof assistant]] software enables the development of [[proofs]] in a manner such that a computer can verify their validity. As proof assistants commonly take the form of a [[programming language]], users face programming-related problems, such as the naturality of expressing ideas and algorithms in the language, usability, and performance. We will investigate these issues as they occur in developing [[Errett Bishop]]’s [[constructive analysis|constructive]] [[Cauchy real number|real numbers]] in the [[Agda]] [[proof assistant]] and [[functional programming language]], with an introduction to each.

\linebreak

* {#KhaliqueFeb2023} 27 Feb 2023

  [[Aeysha Khalique]] (National University of Science and Technology, Islamabad):

  **Computational Tasks through Non-Universal Quantum Computation**

  video: [YT](https://www.youtube.com/watch?v=aWirOZe9AwM)

  > [[quantum mechanics|Quantum Mechanics]] offers phenomena which defy our everyday observation. These are not just theoretical principles but have wide range applications in [[quantum computation]] and [[quantum information]], making some tasks possible which are impossible to be done [[classical physics|classically]]. This talk will take you to the journey through quantum computation, starting from underlying principles to the applications, including my own own contribution to it.

\linebreak

### Mar 2023

\linebreak

* {#NizamaniIqbal2023} 6 Mar 2023

  Altaf Nizamani and Qirat Iqbal (University of Sindh, Pakistan):

  **Quantum Technology with Trapped Ions**

  video: [YT](https://www.youtube.com/watch?v=40_UDRGRP3Q)

  > [[quantum physics|Quantum]] technology is a rapidly advancing field that is poised to revolutionize numerous industries, including [[quantum computing|computing]], communications, [[quantum sensing|sensing]], and [[cryptography]]. At its core, quantum technology relies on the principles of [[quantum mechanics]], which allow for the creation of devices that operate on the quantum level. These devices based on quantum technology can perform tasks that are impossible or prohibitively difficult for [[classical physics|classical]] devices. One of the most promising applications of quantum technology is in [[quantum computing]], quantum communications, and [[quantum sensors]].

  > Trapped ions are one of the promising platform for [[quantum computing]] and sensing. In this approach, individual ions are trapped in a vacuum chamber using [[electromagnetic fields]] and manipulated using [[lasers]] to perform quantum operations. As a quantum system, trapped ions offer several advantages. First, they have long coherence times, meaning that the quantum state of the ion can be preserved for a longer period, allowing for more complex calculations. Second, trapped ions can be precisely controlled and manipulated, allowing for the implementation of high-fidelity quantum gates. Finally, trapped ions can be entangled with one another, allowing for the implementation of quantum algorithms that are impossible to simulate on classical computers. Trapped ions also have great potential as [[quantum sensors]]. By using the properties of the ions to measure changes in their environment, trapped ions can detect minute changes in [[temperature]], [[magnetic fields]], and [[electric fields]], among other things. This makes them useful for applications in precision measurement, such as in atomic clocks, [[gravitational wave]] detection, and magnetometry.

  > One of the major challenges facing trapped ion systems is scalability. While individual ions have been used to perform simple quantum algorithms, scaling the system up to include a large number of ions is a difficult task. However, recent advances in ion trap technology have made it possible to trap larger numbers of ions and transport them in 2D and 3D space to perform more complex operations for quantum computation and sensing experiments. Realization of such devices is not far away. As compared to present atomic clocks, a new generation of quantum-enhanced clocks is now emerging showing significantly improved accuracy. Sensitive physical measurements are an essential component of modern science and technology. Developments in [[quantum sensors]] will outdate their classical counterparts.

  > We will present recent developments and opportunities in quantum technology applications based on trapped ions, including quantum computation and sensing.

\linebreak

* {#MongMar2023} 13 Mar 2023

  [[Roger S. K. Mong]] (Pittsburgh Quantum Institute, USA)

  **Detecting topological order from modular transformations of ground states on the torus**

  cf.: [arXiv:2203.04329](https://arxiv.org/abs/2203.04329)

  > Every two-dimensional [[topological phase]] is associated with some [[topological quantum field theory]] (TQFT), or [more formally](modular+tensor+category#AnyonicTopologicalOrderInTermsOfBraidedFusionCategoriesReferences) a [[modular tensor category]].  The [[ground states]] of a [[topological phase]] [encode information](topological+entanglement+entropy+--+references#CharacterizingTopologicalOrder) about the TQFT, which makes them useful in determining the TQFT data, such as [[anyon]] mutual statistics and self statistics.  For example, many numerical methods for detecting the TQFT [relied on](topological+entanglement+entropy+--+references#CharacterizingTopologicalOrder) the use of minimum entanglement states (MESs), which are the eigenstates of the [[Wilson loop]] operators, and are labeled by the anyons corresponding to their eigenvalues.  Here we revisit the definition of the Wilson loop operators and MESs.  We rederive the [[modular transformation]] of the [[ground states]] purely from the Wilson loop algebra, and as a result, the modular $S$- and $T$-matrices naturally show up in the overlap of MESs.  Importantly, we show that due to the phase degree of freedom of the Wilson loop operators, the MES-anyon assignment is not unique.  This ambiguity means that there are some sets of TQFTs that cannot be distinguished from one another solely by the overlap of MESs.

\linebreak

* 27 Mar 2023

  [[Matthias Christandl]] (Centre for the Mathematics of Quantum Theory, U. Copenhagen):

  **Quantum Software**

  cf.: [arXiv:2009.07161](https://arxiv.org/abs/2009.07161)  [doi:10.1109/TIT.2022.3169438](https://ieeexplore.ieee.org/document/9761242)

  >  In these days, we are witnessing amazing progress in both the variety and quality of platforms for [[quantum computation]] and [[quantum information|quantum communication]]. Since [[algorithms]] and communication protocols designed for traditional 'classical' hardware do not employ the [[superposition principle]] and thus provide no gain even when used on quantum hardware, we are in need of developing specific quantum algorithms and quantum communication protocols that make clever use of the superposition principle and extract a [[quantum advantage]]. "Quantum hardware needs quantum software", so to say. Furthermore, due to noise in the [[qubits]], known as [[decoherence]], an additional quantum-specific software layer is required that emulates a perfect quantum machine on top of a noisy one. I will demonstrate our recent work on this subject with theorems as well data from university and commercial quantum devices.

\linebreak

### Apr 2023

* {#XieApr2023} 3 Apr 2023

  [[Mouzhe Xie]] (University of Chicago)

  **Diamond-based quantum sensor for molecular analytics**

  cf.: [arXiv:2108.04843](https://arxiv.org/abs/2108.04843)

  slides: [[Xie-CQTS-Apr2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=f4qv-H5vkR0)

  > [[quantum sensing|Quantum sensing]] technologies enable some of the most precise [[measurements]] that human beings have ever achieved. In recent years, optically addressable [[nitrogen-vacancy center|nitrogen-vacancy (NV)]] color center hosted by [[diamond]] [[crystal]] has been used as a novel [[quantum sensor]], which has exquisitely sensitive response to local [[magnetic field]] fluctuations. It is therefore capable to perform micro-/nano-scale [[nuclear magnetic resonance|NMR experiments]], manifesting enormous potential to study [[biology|biological systems]] on extremely small sample volume -- even down to single-molecule regime.

  > In this seminar, I will discuss some of the comprehensive efforts to develop [[NV center|NV]]-based [[quantum sensing]] platforms for a wide range of applications in [[chemistry]] and [[biology]]. I will start with a general introduction to [[quantum sensing]] followed by conventional [[NMR]] [[spectroscopy]] as a powerful tool to study biomolecules, as well as their connections to the [[NV center|NV]]-based nanoscale [[NMR]]. I will then introduce a biocompatible surface functionalization architecture for interfacing a diamond quantum sensor with individual intact biomolecules under physiological conditions. A sensing modality based on diamond membrane integrated with flow channel will also be discussed, which is a promising platform for a variety of experiments a molecular, cellular, and even living-organism levels. Finally, I will conclude by providing an outlook on how [[nitrogen-vacancy center in diamond|NV-based]] [[quantum sensing]] platforms, combined with other advanced spectroscopy and microscopy methods, can be utilized to address important biophysical and bioanalytical questions with unprecedented sensitivity and spatial resolution, which will enhance our understanding of molecular interactions and cellular processes and ultimately improve human health.

\linebreak

* {#EconomouApr2023} 3 Apr 2023

  [[Sophia Economou]] (Center for Quantum Information Science and Engineering, Virginia Tech, USA)

  **Control and distribution of entanglement in quantum networks**

  cf.: [arXiv:2212.10820](https://arxiv.org/abs/2212.10820)

  video: [YT](https://www.youtube.com/watch?v=V5pYJLBvNJs)

  > [[quantum network|Quantum networks]] are pursued as a quantum backbone on which to perform secure [[quantum communication]], distributed [[quantum sensing]], and blind [[quantum computation]]. The building blocks of these networks are [[quantum repeaters]], where [[photon|photonic]] [[quantum information]] carriers are generated and [[quantum error correction|error corrected]] through [[interactions]] with matter [[qubits]]. I will describe two paradigms of quantum repeaters and discuss in each case how careful control of a register of [[spin]] qubits can increase the [[quantum entanglement|entanglement]] distribution rate over the network. Specifically, I will describe our recent work on the accurate and fast control of [[NMR|nuclear spin]] memory qubits coupled to spin defects such as the [[NV center]] in diamond. I will also discuss the deterministic generation of photonic 'graph" states from such quantum emitters.

\linebreak

* {#SaleemApr2023} 10 Apr 2023

  Zain Saleem (Argonne National Lab, USA)

  **Classical simulators as quantum error mitigators via circuit cutting**

  cf.: [arXiv:2212.07335](https://arxiv.org/abs/2212.07335)

  video: [YT](https://www.youtube.com/watch?v=hOluuHpU-aY)

  > We introduce an error mitigation framework that mitigates errors in a [[quantum circuit]] using circuit cutting. Our framework can be implemented in polynomial time for a wide variety of quantum circuits. Our technique involves cutting the circuit in such a way that we run the circuit that needs to be executed on the quantum hardware whereas the error mitigation circuit is run on a simulator. We perform error mitigation qubit by qubit and then provide a way to combine the different probabilities from each of the individual qubit error mitigation runs such that the full circuit is error mitigated. We apply our framework to the VQE hardware-efficient ansatz acheiving estimated ground state energies very close to the noise-free simulation results.

\linebreak

* 17 Apr 2023

  [[Piotr Sułkowski]] (University of Warsaw, Poland)

  **Knots-quivers correspondence: summary and update**

  cf. [arXivL2110.13768](https://arxiv.org/abs/2110.13768) following [arXiv:1707.04017](https://arxiv.org/abs/1707.04017), [arXiv:1707.02991](https://arxiv.org/abs/1707.02991)

  > In this talk I will review the [[knots-quivers correspondence]] and mention some recent developments in this regard. The [[knots-quivers correspondence]] is the statement that various [[knot invariant|invariants]] associated to a [[knot]] are encoded in the corresponding [[quiver]]. This statement follows from [[geometric engineering of QFTs|engineering]] both knots and quivers in related [[intersecting brane|brane systems]] in [[string theory]]. Recent developements, which I will mention at least briefly, include understanding the structure of various quivers that correspond to the same knot, using [[topological recursion]] to determine quiver generating series and corresponding quiver A-polynomials, and finding a quiver representation of so-called Z-hat invariants.

\linebreak

* 24 Apr 2023

  Mauro Paternostro (Queen's University Belfast, Ireland):

  **Alice through the looking glass: cavity optomechanics for the study of the foundation of quantum mechanics**

  cf.: [arXiv:2302.08995](https://arxiv.org/abs/2302.08995)

  > I will illustrate how cavity optomechanics is helping us addressing deep  questions on our understanding of the foundations of [[quantum theory]], from  non-equilibrium quantum dynamics to the [[collapse of the wave-function]]. Towards the end of my talk, I will propose an optomechanical pathway for the exploration of the potential quantum nature of gravity.

\linebreak

### May 2023

\linebreak

* 1 May 2023

  [Hichem El Euch](https://scholar.google.com/citations?user=xnUL1qYAAAAJ) (American University of Sharjah, UAE):

  **High-fidelity universal quantum computation with symmetric qubit clusters**

  > Designing a physical device that maintains the error rate for each quantum processing operation low is one of the most arduous issues for the implementation of a scalable [[quantum computer]]. These errors may result from inaccurate quantum manipulation, such as a gate voltage sweeping in [[solid-state physics|solid-state]] [[qubits]] or a [[laser]] pulse duration. [[decoherence|Decoherence]] is usually a manifestation of the interaction with the environment, and it is an entity of the [[quantum system]] which generates errors. Small clusters of [[qubits]] with symmetries can be used to shield part of them from [[decoherence]]. We encode pairs of connected qubits and universal 2-qubit [[quantum gates|logical gates]] using 4-level cores with omega-rotation invariance. We show that symmetry renders logical operations particularly resistant to anisotropic qubit rotations that models some quantum errors. We suggest a scalable method for universal quantum processing in which cores act as quansistors, or quantum transistors. By adjusting their intrinsic variables, quansistors may be dynamically isolated from their environment, providing them the adaptability needed to function as controlled [[quantum memory]] units.

\linebreak

* {#KuprovMay2023} 8 May 2023

  [Ilya Kuprov](https://www.southampton.ac.uk/people/5x97wv/doctor-ilya-kuprov) (University of Southampton):

  **Optimal control of large spin systems**

  cf.: [arXiv:2107.00933](https://arxiv.org/abs/2107.00933), [arXiv:2303.09458](https://arxiv.org/abs/2303.09458)

  video: [YT](https://www.youtube.com/watch?v=FxhaT9s829Q)

  > In [[NMR|magnetic resonance]], optimal control theory is used to generate pulses and pulse sequences that achieve instrumentally difficult objectives (for example, uniform 13C excitation in a 1.2 GHz magnet) with high precision under stringent time and radiofrequency/microwave power constraints. At the moment, the most popular framework is GRAPE (gradient ascent pulse engineering, [10.1016/j.jmr.2004.11.004](https://doi.org/10.1016/j.jmr.2004.11.004)). This lecture reports our recent mathematical and software engineering work on the various extensions and refinements of the GRAPE framework, and on its implementation as a module of Spinach library. Recently implemented functionality includes: fidelity Hessians and regularised Newton-Raphson optimisation, generalised curvilinear waveform parametrisation, prefix and suffix pulse sequences, multi-target and subspace control, keyhole states and subspaces, cooperative pulses and phase cycles, and piecewise-linear control sequences. In keeping with the long tradition, the methods are also directly applicable to quantum technologies outside Magnetic Resonance.

\linebreak

### Sep 2023

* {#SchreiberSep2023} 25 Sep 2023

  [[Urs Schreiber]] (NYUAD, CQTS)

  **Quantum Channels as QuantumState Monad Transformations (Part I)**

  video: [YT](https://youtu.be/EyteOdbSZ5M), [Zm](https://nyu.zoom.us/rec/share/cvJN1WxKAy90-TU2xGGgI_qpr29cXwYnViJK2f7sicBsvZoOfAxYS1oHAURPgtbn.r4soFI_hw6c9Wtok)

  cf.: [[schreiber:The Quantum Monadology|arXiv:2310.15735]]

  > The talk recalls some of the theory of "[[quantum channels]]" and then explains how this is captured by "[[monad (in computer science)|monadic computation]]" with the [[linear logic|linear version]] of the "[[state monad|State monad]]" -- the "[[quantum state monad|QuantumState Frobenius monad]]".

\linebreak

### Oct 2023

* {#NeupertOct2023} 2 Oct 2023

  [[Titus Neupert]] (University of Zurich)

  **Realizing Higher-Order Topology**

  video: [Zm](https://nyu.zoom.us/rec/share/3xppnhEPhej_KTmHq6yWSfGYerz2-78WGz5zXNX4k4NFZtTqWYINWoOns-WZD7nj.61sdBVS2SJMWZYqK)

  cf. [doi:10.1126/sciadv.aat0346](topological+insulator#SchindlerEtAl18)

  > Higher-order topology generalizes the bulk-boundary correspondence of [[topological phases of matter]], by allowing topological modes to be localized at [[manifold with corners|corners]] and hinges instead of edges and surfaces. I will introduce the theory behind this concept, both for noninteracting as well as interacting systems and consecutively discuss two realizations in rather distinct setups. First, as-grown crystals of bismuth, grey arsenic, as well as bismuth bromide are demonstrated to display the essential physics of higher-order topological insulators. Second, it is shown that lattices of so-called Shiba bound states induced by magnetic adatoms in conventional superconductors can be brought into a higher-order superconducting phase. I will report on experimental progress for both system types based on spanning probe as well as transport measurements.

\linebreak

* {#ValeraOct2023} 9 Oct 2023

  [[Sachin Valera]] (NYUAD, [[CQTS]])

  **Topological Quantum Teleportation Without Braiding**

  video: [YT](https://youtu.be/mLKqNMg4ewE), [Zm](https://nyu.zoom.us/rec/share/UKBI5BRiD_Wcg3BjGVpss7_znY7TQ534INlxkwcTAYW0CIxym20o-8a13whOp7XQ.ij2PUcaSzXpz_iC1)

  cf. [arXiv:2303.17700](https://arxiv.org/abs/2303.17700)

  > We present the [[quantum teleportation]] and [[superdense coding]] protocols in the context of [[topological quantum computation|topological]] [[qudits]], as realised by [[anyons]]. The simplicity of our proposed realisation hinges on the [[monoidal category|monoidal structure]] of [[Tambara-Yamagami categories]], which readily allows for the generation of maximally [[quantum entanglement|entangled]] qudits. In particular, we remove the necessity for the [[braiding]] of anyons, an operation which typically underpins any computation. Both protocols find a natural interpretation in the [[string diagram|graphical calculus]] for these categories.

\linebreak

* {#BroadbentOct2023} 16 Oct 2023

  [[Anne Broadbent]] (University of Ottowa, Canada)

  **Quantum Delegation with an Off-the-Shelf Device**

  video: [Zm](https://nyu.zoom.us/rec/share/nzdpfDFPA3928TopuGLljUfHRmbG1UjUOd4Qa1tNqqxDb0btReLKqtfmQQJRF-QR.YZ9wx9uXUevKunh0)

  cf. [arXiv:2304.03448](https://arxiv.org/abs/2304.03448)

  > Given that reliable cloud [[quantum computers]] are becoming closer to reality, the concept of delegation of [[quantum computations]] and its [[software verification|verifiability]] is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size $n$ of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single constant-sized measurement from a predetermined logarithmic-sized input. In the OTS model, we thus picture that a single quantum server does the bulk of the computations, while the OTS device is used as an untrusted and generic verification device, all in a single round.  In this talk, we will show how the delegation of quantum computations can be achieved in the OTS model, and furthermore how to make this protocol zero-knowledge. The emphasis will be on the concepts that contribute to this result; these concepts are drawn from a long line of research related to blind and delegated quantum computation, as well as quantum zero-knowledge proofs. Based on joint work with Arthur Mehta and Yuming Zhao.

\linebreak

* {#PengFuOct2023} 23 Oct 2023

  [[Frank (Peng) Fu]] (Univ. Soth Carolina):

  **Proto-Quipper with Dynamic Lifting**

  video: [YT](https://youtu.be/bBL7rlqbDWM), [Zm](https://nyu.zoom.us/rec/share/IPDDFaZYw-ZJ-g0NAtJ4fixrd-2hjzZeynyiX5WoTdFe_2jHG88J1pUwF8evjsAI.oe71A2fEQ0QJhqpk)

  > [[Quipper]] is a [[functional programming language]] for [[quantum computing]]. Proto-Quipper is a family of languages aiming to provide a [[formal methods|formal foundation]] for Quipper. By virtue of being a [[quantum circuit|circuit]] description language, Proto-Quipper has two separate runtimes: circuit generation time and circuit execution time. Values that are known at circuit generation time are called parameters, and values that are known at circuit execution time are called states. [[dynamic lifting|Dynamic lifting]] is an operation that enables a state, such as the result of a [[quantum measurement|measurement]], to be lifted to a parameter, where it can influence the generation of the next portion of the circuit. As a result, dynamic lifting enables Proto-Quipper programs to [interleave classical and quantum computation](quantum+computation#ClassicalControlQuantumData). In his talk, Dr. Frank will describe how to extend Proto-Quipper-M with dynamic lifting. He will explain the syntax of a language named Proto-Quipper-Dyn. Its type system uses a system of [[modalities]] to keep track of the use of dynamic lifting. Then, he will discuss the [[categorical semantics]] for dynamic lifting. Finally, if time permits, Dr. Frank will give some examples of Proto-Quipper-Dyn programs.

\linebreak

* {#BucherOct2023} 30 Oct 2023

  [[Dominik Bucher]] (Technical University, Munich):

  **Quantum Sensing with Spin Defects in Diamond**

  video: [YT](https://youtu.be/ArN3Ed78sSc), [Zm](https://nyu.zoom.us/rec/share/AT47vaexNQQopnwCZCyZBgSiE47CVNOeEv1K7A8oNLlGAQjo0IAp9zGrswTnn6_f.LvjuOOUeWW_qJw6Y)

  cf.: [arXiv:2306.07593](https://arxiv.org/abs/2306.07593)

  > The [[nitrogen-vacancy center in diamond|nitrogen-vacancy (NV) point defect in diamond]] has emerged as a new class of [[quantum sensors]]. The technique is based on optically detected [[spin resonance|magnetic resonance]] of the NV [[electron|electronic]] [[spins]], which can be used to detect [[magnetic fields]] on unprecedented length scales. In my talk, I will briefly introduce the basics of NV-based [[quantum sensing]], its hardware and review recent highlights in the field. In the second part, I will discuss recent developments in my research group, including quantum sensing in microfluidics for lab-on-a-chip applications and an outlook for single-cell NMR metabolomics.

\linebreak

### Nov 2023

* 06 Nov 2023

  [[Alberto Marchisio]] (NYUAD):

  **Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead**

  video: [Zm](https://nyu.zoom.us/rec/share/WDTV_oHZyZRL8UesI4kan6t0jlhS-FRLx7LM-fKkXfWNTiFC4ZtvAGGJBOFPrERG.pLj3nIsc9Z_nqlKk)

  cf. [arXiv:2310.10315](https://arxiv.org/abs/2310.10315)

  > [[quantum computation|Quantum Computing]] (QC) claims to improve the efficiency of solving complex problems, compared to classical computing. When QC is applied to [[machine learning|Machine Learning]] (ML) applications, it forms a [[quantum machine learning|Quantum Machine Learning]] (QML) system. After discussing the basic concepts of QC and its advantages over classical computing, this talk reviews the key aspects of QML in a comprehensive manner. We discuss different QML algorithms and their domain applicability, quantum datasets, hardware technologies, software tools, simulators, and applications. Valuable information and resources are provided to jumpstart into the current state-of-the-art techniques in the QML field.

\linebreak

### Dec 2023

* {#ShabaniDec2023} 05 Dec 2023

  [[Javad Shabani]] (Center of Quantum Information Physics, NYU):

  **Towards Realization of Protected Qubits Using Topological Superconductivity**

  video: [Zm](https://nyu.zoom.us/rec/share/qGQmot9lKWVPD6N5J-Ajhx3aqJuig7VaU9qe53q4qM-pFNgb9qCVaY_9u4ivLkA2.eimyjBKMzZlZ37fT?startTime=1701781356000)

  cf.: [arXiv:2303.04784](superconductivity#ShabaniEtAl23), [arXiv:2101.09272](superconductivity#ShabaniEtAl22)

  > A central goal in [[quantum computing]] research is to [[topological quantum computation|protect]] and [[quantum error correction|control]] [[quantum information]] from [[noise]]. This talk will provide recent progress on the developing field of [topological superconductivity](superconductivity#AnyonsInTopologicalSuperconductorsReferences) where we can encode information in spatially separated [[Majorana zero modes]] (MZM). We show that [topological superconductivity](superconductivity#AnyonsInTopologicalSuperconductorsReferences) can be achieved in certain hybrid materials where the topological properties are not found in the constituent materials.  These special MZMs are formed at the location of [[topological defects]] (e.g. [[boundary field theory|boundaries]], [[domain walls]],..) and manifest [[anyon|non-Abelian braiding statistics]] that can be used in noise-free [[quantum gate|unitary gate]] operations. We show by engineering a reconfigurable domain wall on a [[Josephson junction]] we can create a scalable platform to study MZM properties and their applications in [[quantum information]] science.

\linebreak

* {#RamanathanDec2023} 11 Dec 2023

  [[Chandrasekhar Ramanathan]] (Dartmouth College, New Hampshire):

  **Quieting Noisy Neighbors: Extending the Coherence Times of Central Electronic Spins in Solids**

  video: [YT](https://youtu.be/FfgT3AAuEt8)

  cf.: [arXiv:arXiv:2311.05396](nitrogen-vacancy+center+in+diamond#BSERTRH23)

  > Isolated [[electron|electronic]] [[spins]] such as donors in silicon and defects like the [[nitrogen-vacancy center in diamond|nitrogen-vacancy (NV) center in diamond]] are promising platforms for some [[quantum system|quantum]] technologies. The [[decoherence]] of these spins is often dominated by interactions with other electronic or nuclear spin species present in their vicinity. For example, silicon-29 nuclear spins can limit the coherence times of donors in silicon, and substitutional nitrogen or P1 centers often limit the coherence times of NV centers in diamond. In this talk I will describe two recent sets of experiments from our group where we are able to extend the coherence times of the central spin by engineering these spin-bath interactions. First, I show how the coherence times of phosphorus donors in silicon are influenced by low-power above-bandgap optical excitation.  Next, I describe the use of dynamical decoupling techniques to suppress NV-P1 interactions in diamond.  In addition to extending coherence times, these decoupling techniques can be used to measure time-dependent magnetic fields, a form of AC-sensing or noise spectroscopy.

\linebreak

### Jan 2024

* {#CapucciJan2024} 22 Jan 2024

  [[Matteo Capucci]] (University of Strathclyde):

  **Para Construction as a Wreath Product**

  slides: [[Capucci-ParaAsWreathProduct.pdf:file]]

  cf. [arXiv:2105.06332](categorical+systems+theory#CGHR22)

  > on the [[para construction]] in [[categorical systems theory]]

\linebreak

* 28 Jan 2024

  [[Alessandra Di Pierro]] (University of Verona):

  **Topological Kernels via Quantum Computation**

  cf. [arXiv:2307.07383](TDA#IMD23)

  > [[topological data analysis|Topological data analysis]] (TDA) enhances the analysis of objects by embedding them into a [[simplicial complex]] and extracting useful global properties such as the [[Betti numbers]], i.e. the number of multidimensional holes, which can be used to define [[kernel methods]] that are easily integrated with existing [[machine-learning]] [[algorithms]]. These [[kernel methods]] have found broad applications, as they rely on powerful mathematical frameworks which provide theoretical guarantees on their performance. However, the [[computation]] of higher-dimensional Betti numbers can be prohibitively expensive on classical hardware, whereas [[quantum computation|quantum algorithms]] can approximate them in polynomial time in the instance size. In this work, we propose a quantum approach to defining topological kernels that is based on constructing Betti curves, i.e. topological fingerprint of [[filtered object|filtrations]] with increasing order.

\linebreak

### Feb 2024

* {#RossFeb2024} 05 Feb 2024

  [[Julien Ross]]:

  **Catalytic Embeddings: Theory and Applications**

  cf.: [arXiv:2305.07720](quantum+circuit+diagram#ACGMMR23)

  > Let $C$ be a [[quantum circuit]] and let $G$ be a set of [[quantum gates]]. A *catalytic embedding* of $C$ over $G$ is a pair $(D,v)$ consisting of a [[quantum state|state]] $v$ and a [[quantum circuit|circuit]] $D$ over $G$ such that for every state $u$ we have $D(u \otimes v) = (C u) \otimes v$. Because the state $v$ is left unchanged by the application of $D$, it is known as a *catalyst*. Catalytic embeddings are useful when the circuit $C$ cannot be exactly represented over the gate set $G$. In such cases, one can leverage the catalyst to implement (any number of occurrences of) $C$ using circuits over $G$.

  > In this talk, I will present the theory of catalytic embeddings and discuss applications to the exact and approximate synthesis of quantum circuits.

\linebreak

* 12 Feb 2025

  [[Chandrashekar Radhakrishnan]] (NYU Shanghai):

  **Theory of Quantum Coherence and Its Application in Quantum Synchronization**

  > [[quantum coherence|Coherence]] is a well-known feature of [[quantum systems]]. An information theoretic investigation of quantum coherence was initiated in [1] from a resource theory perspective. In this talk, I will provide an outline of quantifying coherence, the two different forms corresponding to it namely the intrinsic coherence and local coherence, and trade-off relation between these two types of coherence [2]. As an application, I will talk about the role of quantum coherence in the study of quantum synchronization. First, I will give an overview of synchronization. Then considering an [[open quantum system]] comprising of a two-level system interacting with an external environment, I will show how it exhibits phase preference in the long-time limit. While this phase preference, which we identify as quantum phase localization, shows features like Arnold tongue, which is considered as an identifier for quantum synchronization, I present evidence to show that it is not quantum synchronization [3]. Finally, I will discuss the challenges remaining to be addressed in connecting these two related phenomena of quantum phase localization and quantum synchronization.

  > References:

  > 1. T. Baumgratz, M. Cramer, M. B. Plenio, *Quantifying Coherence*, Phys. Rev. Lett. **113** 140401 (2014) [[arXiv:1311.0275](https://arxiv.org/abs/1311.0275), [doi:10.1103/PhysRevLett.113.140401](https://doi.org/10.1103/PhysRevLett.113.140401)]
  > 2. [[Radhakrishnan Chandrashekar|R. Chandrashekar]], P. Manikandan, J. Segar, [[Tim Byrnes]], *Distribution of quantum coherence in multipartite systems*, Phys. Rev. Lett. **116** 150504 (2016) [[arXiv:1602.00286](https://arxiv.org/abs/1602.00286), [doi:10.1103/PhysRevLett.116.150504](https://doi.org/10.1103/PhysRevLett.116.150504)]
  > 3. Md. Manirul Ali, Po-Wen Chen, [[Radhakrishnan Chandrashekar|R. Chandrashekar]], Physica A 633, 129436 (2024) [[doi:10.1016/j.physa.2023.129436](https://doi.org/10.1016/j.physa.2023.129436)]

\linebreak

* 19 Feb 2024

  [[Venkata S. R. Redrouthu|Venkata SubbaRao Redrouthu]] (NYU AD):

  **The Quantum Symphony: Electron Spin Choreography for Hyperpolarized Nuclear Spin Sensing**

  > Delving into the atomic secrets encoded within [[nucleus|nuclear]] [[spinor|spins]] necessitates a quantum leap in sensitivity. My research endeavors to achieve this leap through Pulsed Dynamic Nuclear Polarization (DNP), an emerging technique that harnesses quantum-controlled [[electron]] spins to hyperpolarize nuclear spins, overcoming inherent sensitivity challenges in [[nuclear magnetic resonance|Nuclear Magnetic Resonance]] (NMR) spectroscopy.

  > In this presentation, I demonstrate a novel [[quantum mechanics|quantum mechanical]] scheme: broad-band pulsed DNP sequences. Comprising carefully choreographed sequences of quantum gates or pulses, each precisely controlled in phase and time, these sequences represent a pivotal advancement beyond conventional DNP methods. Through [[density matrix]]-based theoretical analyses and numerical simulations, I navigate the intricacies of these sequences, offering a deeper comprehension of their foundational principles and the quantum symphony they orchestrate in enhancing nuclear spin sensitivity.

\linebreak

***

\linebreak

## Geometry, Topology & Physics (GTP) Seminar
 {#GTPSeminar}

Weekly seminar, broadly on topics in [[geometry]], ([[algebraic topology|algebraic]]) [[topology]] and [[theoretical physics|theoretical]]/[[mathematical physics]], with focus on applicability to [[high energy physics]]/[[string theory]] and [[quantum systems]].

\linebreak

### Feb 2022

\linebreak

* 02 Feb 2022
  {#AlfonsiFeb2022}

  [[Luigi Alfonsi]] (University of Hertfordshire)

  **Higher quantum geometry and global string duality**

  video: [rec](https://nyu.zoom.us/rec/share/smsfBPZ5n5poB889nfwEzjcb20_SrsgCcFOJBcg492YsxbhCwTz1-8OXxJBGVvxx.CZRA2MziA5nleJWP)

  > In this talk I will discuss the relation between [[higher geometric quantisation]] and the [global geometry underlying](double+field+theory#ReferencesInHigherDifferentialGeometry) [[duality in string theory|string dualities]]. Higher geometric quantisation is a promising framework that makes quantisation of [[classical field theories]] achievable. This can be obtained by quantising either an ordinary prequantum bundle on the ∞-stack of solutions of the equations of motion or a categorified prequantum bundle on a generalised phase space. I will discuss how the higher quantum geometry of string theory underlies the [[topological T-duality|global geometry of]] [[T-duality]]. In particular, I will illustrate how a globally well-defined moduli stack of [[tensor hierarchies]] can be constructed and why this is related to a higher gauge theory with the [[string 2-group]]. Finally, I will interpret the formalism of [[extended field theory|Extended Field Theory]] as an atlas description of the higher quantum geometry of string theory.

\linebreak

* 23 Feb 2022

  [[Dmitri Pavlov]] (Texas Tech University)

  **The geometric cobordism hypothesis**

  video: [rec](https://nyu.zoom.us/rec/share/Q_RbpKr9uMn292h0xtV2_tCbt39l5ZesalIuTE3TejN-fn3y1HyaIMdIY60dhF7S.bivkO70zgwrnRcsD)

  > I will explain my recent work with [[Daniel Grady]] on locality of [[FQFT|functorial field theories]] ([arXiv:2011.01208](https://arxiv.org/abs/2011.01208)) and the geometric [[cobordism hypothesis]] ([arXiv:2111.01095](https://arxiv.org/abs/2111.01095)). The latter generalizes the Baez–Dolan cobordism hypothesis to nontopological field theories, in which bordisms can be equipped with geometric structures, such as smooth maps to a fixed target manifold, Riemannian metrics, [[conformal structures]], [[principal bundles]] [[connection on a principal bundle|with connection]], or [[differential string structure|geometric]] [[string structures]].

  > Applications include a generalization of the [Galatius–Madsen–Tillmann–Weiss theorem](cobordism+category#GMTWTheorem), a solution to a conjecture of Stolz and Teichner on representability of concordance classes of functorial field theories, a construction of [[power operations]] on the level of field theories (extending the recent work of Barthel–Berwick-Evans–Stapleton), and a recent solution by Grady of a conjecture by Freed and Hopkins on deformation classes of reflection positive [[invertible field theories]]. If time permits, I will talk about the planned future work on nonperturbative quantization of functorial field theories and generalized Atiyah–Singer-style index theorems.

\linebreak

### Mar 2022

\linebreak

* 08 March 2022

  [[David White]] (Denison University, USA):

  **The Kervaire Invariant, multiplicative norms, and N-infinity operads**

  video: [rec](https://nyu.zoom.us/rec/share/GGfyckAXd17ket9Oc24UiymACRyk68rkEHYywkN5q8fzLrVBq_0uUKyRAppbgBHR.8mbsXTDkkeCeWRbp)

  > In a 2016 Annals paper, Hill, Hopkins, and Ravenel solved the [[Arf-Kervaire invariant problem|Kervaire Invariant One Problem]] using tools from [[equivariant stable homotopy theory]]. This problem goes back over 60 years, to the days of Milnorand the discovery of exotic smooth structures on spheres. Of particular importance it its solution were equivariant commutative ring spectra and their multiplicative norms. A more thorough investigation of multiplicative norms, using the language of operads, was recently conducted by Blumberg and Hill, though the existence in general of their new “N-infinity” operads was left as a conjecture. In this talk, I will provide an overview of the Kervaire problem and its solution, I will explain where the [[operads]] enter the story, and I will prove the Blumberg-Hill conjecture using a new model structure on the categoryof equivariant operads.

\linebreak

* 16 March 2022

  [[Guo Chuan Thiang]] (Beijing University)

  **How open space index theory appears in physics**

  video: [rec](https://nyu.zoom.us/rec/share/JbJ05VbCnnfrhsr0cpVzyPTYBzHfAClCfaA7HXNhk5m44aRSx4FLRDvpK0Isp580.QFIVD3Thyt4bvRhn)

  > The incredible stability of [[quantum Hall effect|quantum Hall systems]] and [[topological phase of matter|topological phases]] indicates protection by an underlying [[index theorem]]. In contrast to Atiyah-Singer theory for compactified problems, what is required is an index theory on noncompact Riemannian manifolds, with interplay between discrete and continuous spectra. Input data comes not from a topological category a la [[TQFT]], but a metrically-coarsened one. This is the subject of coarse geometry and index theory, and I will explain their experimental manifestations.

\linebreak

* 30 March 2022
  {#MartinPalmerMarch22}

  [[Martin Palmer]] (Romanian Academy)

  **Mapping class group representations via Heisenberg, Schrödinger and
Stone-von Neumann**

  [zoom link](https://nyu.zoom.us/rec/play/nqQSRLTINmsD32Bp68ysikC1yod5PKKneHckP-yhY4Z-sDbuCCCNn5UGIX7RMN_KPHkMgNPRfy2nGC2L.CufxX4yp7T9DFicw?autoplay=true&startTime=1648645579000)

  > One of the first interesting [[braid group representation|representations of]] the [[braid groups]] is the [[Burau representation]]. It is the first of the family of Lawrence representations, defined topologically by viewing the braid group as the [[mapping class group]] of a punctured disc. Famously, the Burau representation is almost never faithful, but the $k = 2$ Lawrence representation is always faithful: this is a celebrated theorem of Bigelow and Krammer and implies immediately that braid groups are linear (act faithfully on finite-dimensional vector spaces). Motivated by this, and by the open question of whether mapping class groups are linear, I will describe [recent joint work with Christian Blanchet and Awais Shaukat](https://arxiv.org/abs/2109.00515) in which we construct analogues of the  awrence representations for mapping class groups of compact, orientable surfaces. Tools include twisted Borel-Moore homology of con guration spaces, Schrödinger representations of discrete Heisenberg groups and the Stone-von Neumann theorem.

\linebreak

### Apr 2022

\linebreak

* 06 April 2022

  [[Kiyonori Gomi]] (Tokyo Institute of Technology)

  **Differential KO-theory via gradations and mass terms**

  [zoom link](https://nyu.zoom.us/rec/play/7bZ5QFOvN2cUPSEQ2-8F1Ek8-SjV7ibQbBJANgPd1jJKP5Fv3J664ck86Rin-74Sv6HLOxSrhqOhVx4u.4Dxb1bbc5C0fN-nB?autoplay=true&startTime=1649246546000)

  > [[differential cohomology|Differential generalized cohomologies]] refine generalized cohomologies on manifolds so as to retain information on differential forms. The aim of my talk is to describe formulations of [[differential K-theory|differential]] [[KO-theory]] based on gradations and [[mass terms]]. The formulation based on mass terms is motivated by a conjecture of Freed and Hopkins about a classification of [[invertible quantum field theories]] and by a model of the [[Anderson dual]] of [[cobordism cohomology|cobordism theory]] given by Yamashita and Yonekura. I will start with an account of this background, and then describe the formulation of [[differential K-theory|differential]] [[KO-theory]]. In the formulation a key role is played by a uperconnection associated to a mass term. This is a joint work with [[Mayuko Yamashita]].

\linebreak

* 13 April 2022

  [[Mario Velásquez]] (Universidad Nacional de Colombia)

  **The Baum-Connes conjecture for groups and groupoids**

  > In this talk we present some basics definitions around the [[Baum-Connes conjecture]] in the context of groups and groupoids, in particular we define the reduced $C^\ast$-algebra $C_r^*(G)$ of a groupoid G. When a group (or groupoid) satisfies this conjecture we present how we can compute the topological K-theory of $C_r^*(G)$ via a classifying space. We also present some explicit computations and an application about Fredholm boundary conditions in manifolds with corners.

\linebreak

* 27 April 2022

  [[Amnon Neeman]] (Australian National University)

  **Bounded t-structures and stability conditions**

  > We will give a gentle introduction to the topic. We will review the definitions of [[derived category|derived]] and [[triangulated categories]], of [[t-structures]] an of [[Bridgeland stability condition|stability conditions]]. The only new result will come at the very end of the talk, a theorem saying that there are no stability condition on the derived category of bounded complexes of vector bundles on a singular scheme.

\linebreak

### May 2022

\linebreak

* 11 May 2022
  {#AlexFokMay22}

  [[Alex Fok]] (NYU Shanghai)

  **Equivariant twisted KK-theory of noncompact Lie groups**

  > The [[Loop Groups and Twisted K-Theory|Freed-Hopkins-Teleman theorem]] asserts a canonical link between the [[twisted ad-equivariant K-theory|equivariant twisted K-theory]] of a [[compact Lie group]] equipped with the conjugation action by itself and the representation theory of its loop group. Motivated by this, we will present results on the [[twisted equivariant K-theory|equivariant twisted]] [[KK-theory]] of a noncompact semisimple Lie group $G$. We will give a geometric description of generators of the equivariant twisted KK-theory of G with equivariant correspondences, which are applied to formulate the geometric quantization of quasi-Hamiltonian manifolds with proper G-actions. We will also show that the Baum-Connes [[assembly map]] for the $C^\ast$-algebra of sections of the Dixmier-Douady bundle which realizes the twist is an isomorphism, and discuss a conjecture on representations of the loop group $L G$. This talk is based on joint work with [[Mathai Varghese]].

\linebreak

### Sep 2022

\linebreak

* 21 Sep 2022

  [[Grigorios Giotopoulos]] (NYU Abi Dhabi)

  **Braided Homotopy Lie Algebras and Noncommutative Field Theories**

  cf.: [arXiv:2112.00541](https://arxiv.org/abs/2112.00541)

\linebreak

* 28 Sep 2022
  {#DavidJMyers22}

  [[David Jaz Myers]] (NYU Abu Dhabi, [[CQTS]])

  **Objective Cohomology -- Towards topological quantum computation**

  slides: [[DavidJazMyers-ObjectiveCohomology-220928.pdf:file]]

  > In this talk, we will see the [[homotopy type theory]] point of view on defining pptwisted cohomology]] classes by means of [[bundle gerbes]]. We'll take an increasingly less leisurely tour up the tower of cohomology degrees, seeing [[group character|characters]], [[principal bundles]],  [[central extensions]], and [[characteristic classes]] along the way. Finally, we will go through the construction of the cohomology of the [[braid groups]] valued in the [[complex numbers]], twisted by a complex [[group character|character]] of the braid group. Through the [work of many people](Knizhnik-Zamolodchikov+equation#BraidRepresentationsViaTwisteddRCohomologyOfConfigurationSpaces), and in particular Feigin, Schechtman, Varchenko, the actions of the braid group of $d$ "defects" on the twisted complex cohomology of the braid group of $n$ "particles" is the monodromy action of the [[Knizhnik-Zamolodchikov connection]] on a space of [[conformal blocks]]. At [[CQTS]] [[schreiber:Topological Quantum Programming in TED-K|we use this]] as a way to go from abstract [[homotopy type theory]] to protocols for [[topological quantum computation]].

\linebreak

### Oct 2022

* 05 Oct 2022
  {#CloughSep22}

  [[Adrian Clough]] (NYU Abu Dhabi, [[CQTS]])

  **The smooth Oka principle**

  video: [rec](https://zoom.us/rec/play/zbBe8bZrCUaHoSKmBc00aaDZcSOT4rq_MM-HVjGt7vDt9Lvd_3mNA05lwPUmepOB1Ra5lXor41XLB1Ag.qmFDwX1tjPy8M4sh?continueMode=true&iet=Kmr3DOjJb1qTnxTfDovisY_suPVrnxLj4u8WYsw0cXk.AG.qC5ky7Wu8GA5vScNB42aYhzlh1gg9tOyF6lgg7xSIdAOq2frtqqnFMVoQW_hHB4vSBNQj0Eq69rPm6eLCjo-CWSw9FxWBzV5NM-oQ1PDwEbqMcE.eNG8nnvyuDV2rxZHIc2GvA.TT-h-eb0A8dPgKDq&_x_zm_rtaid=XdmVwP1bTcqHQXfyCJBkGQ.1667379052963.a3fc19b1a88d43cc4ce525059f7ce542&_x_zm_rhtaid=807)

  notes: [pdf](https://github.com/adrianclough/adrianclough.github.io/raw/main/The%20smooth%20Oka%20principle%206.pdf)

  cf.: [Clough 2021](shape+via+cohesive+path+∞-groupoid#Clough21)

> The [[(infinity,1)-topos|infinity topos]] of [[smooth infinity-groupoid|differentiable sheaves]] contains all [[smooth manifolds]] as a [[full sub-(infinity,1)-category|full subcategory]] and has excellent formal properties. In particular, it admits an [[shape modality|intrinsic notion]] of [[underlying]] [[homotopy type]] of any [[smooth infinity-groupoid|differentiable sheaf]], which coincides with classical constructions such as taking smooth total [[singular simplicial complexes|singular complexes]]. Moreover, there is a canonical sense in which the [[mapping stack|mapping sheaf]] between any two [[smooth infinity-groupoid|differentiable sheaves]] may have the correct homotopy type. This latter notion is [reminiscent of](shape+via+cohesive+path+∞-groupoid#ConsequenceSmoothOkaPrinciple) the [[Oka principle]] in [[complex geometry]]. In this talk I will show how to exhibit the [Oka principle in the smooth setting](shape+via+cohesive+path+∞-groupoid#ConsequenceSmoothOkaPrinciple) using [[model category|model structures]] and other [[homotopical algebra|homotopical calculi]] on the [[(infinity,1)-topos|infinity topos]] of [[smooth infinity-groupoids|differentiable sheaves]].

\linebreak

* 12 Oct 2022

  [Salah Mehdi](https://nyuad.nyu.edu/en/academics/divisions/science/faculty/salah-mehdi.html) ([U Lorraine](https://mehdi.perso.math.cnrs.fr/) and [NYU Abu Dhabi](https://nyuad.nyu.edu/en/academics/divisions/science/faculty/salah-mehdi.html))

  **Algebraic and geometric aspects of the Dirac equation**

  > on [arXiv:2102.03562](https://arxiv.org/abs/2102.03562)

\linebreak

* {#KongOct2022} 19 Oct 2022

  [[Liang Kong]] (SIQSE and SUST)

  **Topological Wick Rotation and Holographic Dualities**

  video: [rec](https://zoom.us/rec/play/mrTkGgyx0G9iAjHUoDTGgZaQxdFMpbgsu2gD8N-YPm1lhvw4qsPfRmieIg0VN9cHEbhVCoH0EG41shSi.QpERsN3hWIRaHQ4L?continueMode=true&iet=RGyJowYxQz9V9d_wDNIhAuiEFxGKQ2-F4E-ZX0oPA4k.AG.5P3AQnZmpSkg-Q2LjEK42pRDG4QEtAwPi81dF_RQ9Lkt-dTS5N4qZEvt6fJqGFFtk-3m20u6tytOkKBhPnj9_2QkSj6NXj0nPfVMY3Faw1qpj5k.9w1MqMWhKVo1zF1e-MCQhA.ZfTkXvGYighAp0vK&_x_zm_rtaid=XdmVwP1bTcqHQXfyCJBkGQ.1667379052963.a3fc19b1a88d43cc4ce525059f7ce542&_x_zm_rhtaid=807)

  slides: [[Kong-TalkAtCQTS-20221019.pdf:file]]

  > on [[topological order]], [[braided fusion categories]] and the [[holographic principle]]

\linebreak

* {#SchreiberOct2022} 26 Oct 2022

  [[Urs Schreiber]] (NYU Abu Dhabi, [[CQTS]])

  **Quantum Programming via Linear Homotopy Types**

  slides: see those for [external talk at  QTML2022](#QTML22)

  > We first recall basic notions of [[quantum logic gates]] and [[quantum circuits]], highlighting the conceptually more subtle issues of classical effects ([[quantum measurement|measurements]]) and control ([[quantum state preparation|state preparation]]). Then we briefly review the formulation of [[monad in computer science|computational effects and control]] via [[adjoint functor|adjunctions]] and [[monads]] on [[data type]] [[type systems]], in order to finally indicate basics of [our observation](#QTML22) that in any decent type system which has *[[dependent linear type theory|classically dependent linear data types]]*, the relevant language structures for describing classical/quantum effects emerge naturally.

### Nov 2022

* 09 Nov 2022

  [[Zhen Huan]] (HUST)

  **Twisted Real quasi-elliptic cohomology**

  video: [rec](https://zoom.us/rec/play/_2MIenxSff2vBZeFPO8lV6g_lyLgrUEBDP5Au7tySNyeJpeLeXfZ96ZBkgKs7wNYAnBDauB4atzVJAt-.McANEtFgQHFACmbr?_x_zm_rhtaid=966&_x_zm_rtaid=F4VKJYOLRDu8ouQdfmDz3w.1668757869896.554b5189e89fa9af0846d97599b6bf49&autoplay=true&continueMode=true&iet=6_ddkV5u8UGa9M9U4dDvH2SN55OyZgmZiCrQZ6wbo4E.AG.Gp56JL6y5Z3naAtSVPOGAHkLGEPMDtxPB370GxyQz_EIJOEq1ylk0bXAowqSDnPSYr62xiX92tLdNLdbchq-w5Vhavx5UCPbjfaCIIObE183OI8.142oNpQmC8JiJOzcA4eIXw.O0nEkHAMvD5awvgi&startTime=1667999236000)

  >  [[quasi-elliptic cohomology|Quasi-elliptic cohomology]] is closely related to [[Tate K-theory]]. It is constructed as an object both reflecting the geometric nature of [[elliptic curves]] and more practicable to study than most [[elliptic cohomology|elliptic cohomology theories]]. It can be interpreted by [[Huan's inertia orbifold|orbifold loop spaces]] and expressed in terms of [[equivariant K-theory|equivariant K-theories]]. We formulate the complete [[nLab:power operation]] of this theory. Applying that we prove the finite subgroups of the [[Tate curve]] can be classified by the Tate K-theory of [[symmetric groups]] modulo a certain transfer ideal. In this talk we construct twisted Real quasi-elliptic cohomology as the [[twisted K-theory|twisted]] [[KR-theory]] of [[free loop  orbifold|loop groupoids]]. The theory systematically incorporates loop rotation and reflection. After establishing basic properties of the theory, we construct Real analogues of the string power operation of quasi-elliptic cohomology. We also explore the relation of the theory to the Tate curve. This is joint work with [[Matthew Young]]. [[arXiv:2210.07511](https://arxiv.org/abs/2210.07511)]

\linebreak

* {#FoitNov2022} 23 Nov 2022

  [[Valentino Foit]] (NYUAD)

  **Brownian loops and conformally invariant systems**

  slides: [[Foit_CQTS-Nov2022.pdf:file]]

  video: [rec](https://nyu.zoom.us/rec/play/DxmoQSXAGXA331jrD4isyOJrmpvTdgmRnaDLeD3gAabO1v6zlTjYNcxPT74SS0VDtWzbiRyYQTltw9vp.dI1nqe74UCpaouu_?continueMode=true&_x_zm_rtaid=kQZZ5EfLRZiMesvQXmFYBg.1669295362714.dd968befceb1ba32e41f0349dfb7ca0f&_x_zm_rhtaid=14), [YT](https://www.youtube.com/watch?v=23A-jU_oiYc)

  > The [[Brownian loop soup]] (BLS) is a stochastic system that is constructed from random loops in the plane and is invariant under conformal transformations. Correlation functions of certain observables can be used to formulate the BLS as a Conformal Field Theory (CFT). I will give an overview of CFTs in two dimensions and point out their relation to certain stochastic systems. Then I will discuss the BLS including some recent progress, such as the operator content, the continuous spectrum, and hints of an extended symmetry algebra.

\linebreak

* 30 Nov 2022

  [[Allan Merino]],

  **Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup**

  video: [rec](https://nyu.zoom.us/rec/play/oYJuNiMXDAurst6yAENgOX7PgADZXx6CGL_cp0zppoSU41Dz8Xw9a4oOHdf8tesb-1HvoY_S3vhCwSRK.YR9-fiYNemEmWTg2?continueMode=true&_x_zm_rtaid=sLgowcVYSQCvxs8pgmL7BA.1670394507008.c2f106fca7fc8238463055aaaac2faee&_x_zm_rhtaid=940)

  > One of the main problems in representation theory is to determine the set of equivalence classes of irreducible unitary representations of a Lie group. Using the Weil representation, [[Roger Howe]] established a one-to-one correspondence (known as the local theta correspondence) between particular representations of two subgroups $G$ and $G'$ forming a [[reductive dual pair|dual pair]] in $Sp(W)$. This correspondence provides a nice way to construct unitary representations of small Gelfand-Kirillov dimension.

  > In his wonderful paper "Remarks on classical invariant theory", Roger Howe suggested that his classical duality should be extendable to superalgebras/supergroups. In a recent work with Hadi Salmasian, we obtained a classification of irreducible reductive dual pairs in a real or complex orthosymplectic Lie supergroup $SpO(V)$. Moreover, we proved a "double commutant theorem" for all dual pairs in a real or complex orthosymplectic Lie supergroup.

  > In my talk, I will spend quite some time explaining how the [[Howe duality]] works in the symplectic case and then talk about the results we obtained in our paper with H. Salmasian. [[arXiv:2208.09746](https://arxiv.org/abs/2208.09746)]

\linebreak

### Dec 2022

* {#RiehlDec2022} 07 Dec 2022

  [[Emily Riehl]] (Johns Hopkins University)

  **$\infty$-Category theory for undergraduates**

  video: [rec](https://nyu.zoom.us/rec/play/uhPi_E6RhKKkV5NO5ZCxX-jRBZnRwgPCbkNWi4flBWujKQb6zeecTWi9zhYcSaYRL_M_nPW-tJ7DPuoi.yb4KL0WhGoxp02ii?continueMode=true&_x_zm_rtaid=JLv1PfDKQf6S_2mHA5ukTg.1670481932564.2228c1085c8887067af0b733ac87a817&_x_zm_rhtaid=543), [YT](https://www.youtube.com/watch?v=7g2rkiFsbXo)

  cf.: [arXiv:2302.07855](https://arxiv.org/abs/2302.07855), [AMS Notices](infinity1-category#Riehl23)

  > At its current state of the art, [[(infinity,1)-category theory|$\infty$-category theory]] is challenging to explain even to specialists in closely related mathematical areas. Nevertheless, historical experience suggests that in, say, a century's time, we will routinely teach this material to undergraduates. This talk describes one dream about how this might come about --- under the assumption that 22nd century undergraduates have absorbed the background intuitions of [[homotopy type theory]]/[[univalent foundations]].

\linebreak

* {#FinsterDec2022} 14 Dec 2022

  [[Eric Finster]] (University of Birmingham)

  **The $(\infty,1)$-category of Types**

  slides: [[Finster-CQTS2022.pdf:file]]

  video: [rec](https://nyu.zoom.us/rec/share/MFJT2B2SX8XUsB0n4z-hwMKb-mxyenQhE5HgBC72qIdHb-ixm7FqQ_KN8hDa0YWl.tEp5kHPzkef1ZDHU), [YT](https://www.youtube.com/watch?v=RFm1nz6YV_U)

  > A major outstanding difficulty in [[homotopy type theory|Homotopy Type Theory]] is the description of [[coherence law|coherent]] [[nLab:higher algebra|higher algebraic structures]]. As an example, we know that the algebraic structure possessed by the collection of types and functions between them is *not* a traditional 1-category, but rather an [[(infinity,1)-category|(∞,1)-category]]. In this talk, I will describe how the addition of a finite collection of additional definitional equalities designed to render the notion of "[[opetopic type theory|opetopic type]]" definable in fact allows one to construct the [[(∞,1)-category]] structure on the [[universe of types]].

\linebreak

### Jan 2023

* {#Creutzig23} 25 Jan 2023

  [[Thomas Creutzig]] (University of Alberta):

  **Representation Theory of affine vertex algebras**

  > Recently there has been increased interest in non-[[semisimple]] [[braided tensor categories]]. [[vertex operator algebra|Vertex algebras]] are a rich source of such categories and so I will give an overview on the [[representation theory]] of [[affine Lie algebra|affine]] vertex algebras with a focus on the simplest example of [[sl(2)|$\mathfrak{sl}(2)$]]. As we will see, already in this example quite rich and non-semisimple categories of modules appear.

\linebreak

* {#MyersFeb2023} 01 Feb 2023

  [[David Jaz Myers]] ([[CQTS]] @ NYU Abu Dhabi):

  **Simplicial, Differential, and Equivariant Homotopy Type Theory**

  video: [rec](https://nyu.zoom.us/rec/play/uk0LXy5ub2YUpJPhYq5p7GvpZ2I8_CZaWHSpWvZgwuUyHeWjXgUj2AQd21K1WSJo90V5DrE0BVhl7NuB.QbyHhtPHaJVQUj2A?continueMode=true&_x_zm_rtaid=Xyx9WZFLQzyRzu0Oh-2mNQ.1675318497581.13147cc7929a947e978b29124a207f98&_x_zm_rhtaid=938), [YT](https://www.youtube.com/watch?v=4bj0M2L95Kw)

  cf.: [arXiv:2301.13780](https://arxiv.org/abs/2301.13780)

  > on [[cohesive homotopy type theory]] with two commuting notions of [[cohesion]]

\linebreak

### Feb 2023

* {#HuangFeb23} 8 Feb 2023

  [[Ruizhi Huang]] (Chinese Academy of Sciences)

  **Fractional structures on bundle gerbe modules and fractional classifying spaces**

  video: [rec](https://nyu.zoom.us/rec/play/DS4ghcqqDrUKn_Kcpl-KmQumvcTBYW3x6SLusPAsrbA7SOEpBJf-nlHybxr4vYAt--LRzaMEDE6a8Cjl.HHF82LMYy6a5lhxT?continueMode=true&_x_zm_rtaid=O2NFaJO9RFmzSIlf3qPwOg.1675927086260.18ab992663c527fc76735a5e42797f27&_x_zm_rhtaid=212)

  cf.: [arXiv:2203.14439](https://arxiv.org/abs/2203.14439)

  > Both [[higher structures]] and [[bundle gerbe modules]] play important roles in modern [[geometry]] and [[mathematical physics]]. [[bundle gerbe module|Bundle gerbe modules]] is a [[twisted vector bundle|twisted version]] of [[vector bundles]], and was introduced by Bouwknegt-Carey-Mathai-Murray-Stevenson in 2002. In particular, they introduced the [[twisted Chern character]] from the perspective of [[Chern-Weil theory]]. In a recent joint work with Han and Mathai, we study the [[homotopy theory]] aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's [[rational homotopy theory]], we realize the twisted Chern classes at the level of [[classifying spaces]]. The construction suggests a notion, which we call fractional U-structure serving as a universal framework to study the twisted Chern classes of torsion bundle gerbe modules from the perspective of classifying spaces. Based on this, we introduce and study higher fractional structures on torsion bundle gerbe modules parallel to the higher structures on ordinary vector bundles.

\linebreak

* 15 Feb 2023

  [[Eugene Rabinovich]] (University of Notre Dame, USA)

  **Classical Bulk-Boundary Correspondences via Factorization Algebras**

  cf. [arXiv:2202.12332](https://arxiv.org/abs/2202.12332) (a form of [[Poisson holography]])

  > A [[factorization algebra]] is a [[cosheaf]]-like local-to-global object which is meant to model the structure present in the [[observables]] of [[classical field theory|classical]] and [[quantum field theories]]. In the [[BV-formalism|Batalin-Vilkovisky (BV) formalism]], one finds that a factorization algebra of classical observables possesses, in addition to its factorization-algebraic structure, a compatible [[Poisson bracket]] of cohomological degree +1.  Given a "sufficiently nice" such factorization algebra on a [[manifold]] $N$, one may associate to it a factorization algebra on $N\times \mathbb{R}_{\geq 0}$.

  > The aim of the talk is to explain the sense in which the latter factorization algebra "knows all the classical data" of the former.

  > This is the bulk-boundary correspondence of the title. Time permitting, we will describe how such a correspondence appears in the [[deformation quantization]] of [[Poisson manifolds]].

\linebreak

* {#KozlovFeb2023} 22 Feb 2023

  [[Dmitry Kozlov]]

  **Applied and Computational Topology**

  * video: [YT](https://www.youtube.com/watch?v=GB8i8foPw4w)

  > We will give a brief introduction to the subject of [[applied topology|Applied]] and [[computational topology|Computational Topology]]. The survey of the subject's main ideas and tools will be complemented with applications to [[discrete mathematics]] and to theoretical [[distributed computing]]. We will conclude with stating an open problem in combinatorial topology which is related to the complexity of the Weak Symmetry Breaking distributed task.

\linebreak

### Mar 2023

* {#MuellerMar2023} 1 Mar 2023

  [[Lukas Müller]]

  **Deformation quantization and categorical factorization homology**

  video: [YT](https://www.youtube.com/watch?v=kC488wISPX4)

  cf. [arXiv:2107.12348](factorization+homology#KellerMüller23)

  > [[moduli space of flat connections|Moduli spaces of flat principal bundles]] on [[surfaces]] are a prominent object in [[mathematical physics]], [[algebraic geometry]] and [[geometric representation theory]]. In particular they are the [[phase space]] of 3-dimensional [[Chern-Simons theory]] on a surface times an interval and hence equipped with a [[symplectic structure]] going back to the work of [[Atiyah]] and [[Bott]]. Various [[deformation quantizations]] of the [[algebra of functions]] have been constructed. Ben-Zvi, Brochier & Jordan constructed "local to global" quantizations using [[factorization homology]] of representation categories of [[quantum groups]]. Local to global constructions in this setting only work if the [[higher geometry|higher geometric]] [[higher structure|structure]] of the moduli space of flat bundles is taken into account, i.e. it is treated as a [[moduli stack]]. In this setting the algebra of functions does not contain all the information and should be replaced by the category of [[quasicoherent sheaves]].

  > In my talk we will explore [[categorifications]] of deformation quantization as deformations of [[symmetric monoidal categories]] (algebras over the [[E-infinity operad|$E_\infty$-operad]]) into $E_i$-categories and their interplay with factorization homology. The main result is that 2-dimensional factorization homology "commutes" with [[quantization]] in a way relating $E_0$-quantizations to braided ($E_2$) quantizations. We will illustrate our results with examples from [[Poisson geometry]] and [[quantum groups]]. As a specific application we show that deformation quantizations of the moduli space of flat bundles based on Kontsevich integrals constructed by Li, Bland & Ševera are equivalent to quantizations constructed by Alekseev, Grosse & Schomerus based on quantum groups. The talk is based on joint work in progress with Eilind Karlsson, [[Corina Keller]], and [[Jan Pulmann]].

\linebreak

* {#QuickMar2023} 8 Mar 2023

  [[Gereon Quick]] (Norwegian University of Science and Technology):

  **Geometric Hodge filtered complex cobordism**

  cf.: [arXiv:2210.13259](https://arxiv.org/abs/2210.13259)

  video: [YT](https://www.youtube.com/watch?v=pMu0gT5kIBo)

  > [[differential cohomology|Differential cohomology theories]] on [[smooth manifolds]] play an important role in [[mathematical physics]] and other areas of [[mathematics]]. In their [[Quadratic Functions in Geometry, Topology, and M-Theory|seminal work]], [[Mike Hopkins|Hopkins]] and [[Isadore Singer|Singer]] showed that every [[Whitehead-generalized cohomology theory|topological cohomology theory]] has a differential refinement. In this talk, I will first report on joint work with [[Mike Hopkins]] on a similar refinement of [[complex cobordism]] on [[complex manifolds]] which takes the [[Hodge filtration]] into account. I will then present joint work with [[Knut Haus]] in which we give a concrete geometric cycle model for this theory. This allows us to give a concrete description of an [[Abel-Jacobi map|Abel-Jacobi type]] [[secondary characteristic class|secondary invariant]] for topologically trivial cobordism cycles.

\linebreak

* {#MartinsMar2023} 29 Mar 2023

  [[João Faria Martins]] (Leeds University, UK)

  **Quinn Finite Total Homotopy TQFT as a once-extended TQFT**

  cf.: [arXiv:2301.02491](https://arxiv.org/abs/2301.02491)

  video: [YT](https://www.youtube.com/watch?v=K2kSKxr-I7Q)

  > [Quinn Finite Total Homotopy TQFT](HQFT#Quinn95) is a [[TQFT]] defined for any dimension, $n$, of space, and that depends on the choice of a [[pi-finite homotopy type|homotopy finite space]], $B$, (e.g. $B$ can be the [[classifying space]] of a finite group or of a finite 2-group). I will report on ongoing joint work with [[Tim Porter]] on once-extended versions of Quinn Finite total homotopy TQFT, taking values in the ([[symmetric monoidal category|symmetric monoidal]]) [[bicategory]] of [[groupoids]], linear [[profunctors]], and [[natural transformations]] between profunctors. The construction works in all dimensions, thus in particular it yields (0,1,2), (1,2,3) and (2,3,4)-[[extended TQFTs]], any time we are given a homotopy finite space $B$. I will show how to compute these once-extended TQFTs for the case when $B$ is the classifying space of a finite [[strict omega-groupoid]], represented by a [[crossed complex]].

\linebreak

### Apr 2023

* {#RoviArp2023} 05 Apr 2023

  [[Carmen Rovi]] (Loyola University, Chicago):

  **Relating cut and paste invariants and TQFTS**

  cf.: [arXiv:1803.02939](https://arxiv.org/abs/1803.02939)

  video: [YT](https://www.youtube.com/watch?v=lD8wQhwyrdg)

  > In this talk, we will be concerned with a relation between [[TQFTs]] and the [cut-and-paste SKK invariants](scissors+congruence#CutAndPasteOfManifolds) introduced by [Karras, Kreck, Neumann, and Ossa](scissors+congruence#KarrasKreckNeumannOssa73). Cut-and-paste SKK  invariants are [[functions]] on the set of [[smooth manifolds]] whose values on [[cutting and pasting of manifolds|cut-and-paste equivalent manifolds]] differ by an error term depending only on the gluing [[diffeomorphisms]]. I will present a natural [[group homomorphism]] between the [[group]] of [[invertible TQFTs]] and the group of SKK invariants and describe how these groups fit into a [[split exact sequence]]. We conclude in particular that all positive real-valued SKK invariants can be realized as restrictions of [[invertible TQFTs]].

\linebreak

* {#LudewigApr2023} 12 Apr 2023

  [[Matthias Ludewig]] (University of Regensburg, Germany)

  **The spinor bundle on loop space and its fusion product**

  cf.: [arXiv:2206.09797](https://arxiv.org/abs/2206.09797)

  video: [YT](https://www.youtube.com/watch?v=iiRm47HavRU)

  > We will discuss the definition of the [[stringor bundle|spinor bundle on loop space]] and the construction of its fusion product, as suggested in a [2005 preprint by Stolz and Teichner](What+is+an+elliptic+object%3F#StolzTeichner2005). This is based on [work by Kristel and Waldorf](stringor+bundle#KristelLudewigWaldorf22), involving some simplifications and additions due to myself.

\linebreak

* {#GwilliamApr2023} [[Owen Gwilliam]] (University of Massachusetts, Amherst, USA)

  **A bulk-boundary correspondence with factorization algebras**

  cf.: [arXiv:2001.07888](https://arxiv.org/abs/2001.07888)

  video: [YT](https://www.youtube.com/watch?v=ovCNweQQ2js)

  > [[factorization algebra|Factorization algebras]] provide a flexible language for describing the [[observables]] of a [[perturbative quantum field theory]], as shown in joint work with [[Kevin Costello]]. In [joint work with Eugene Rabinovich and Brian Williams](AdS3-CFT2+and+CS-WZW+correspondence#GwilliamRabinovichWilliams2022), we extended those constructions to a [[manifold with boundary]] for a special class of theories that includes, as an example, a [[perturbative quantum field theory|perturbative]] version of the correspondence between chiral [[circle group|$U(1)$]] [[current algebra|currents]] on a [[Riemann surface]] and abelian [[Chern-Simons theory]] on a [[bulk]] [[3-manifold]]. (These methods extend to [[interacting field theory|interacting]] theories, thanks to the thesis of Rabinovich.) Given time, I'll sketch a systematic higher dimensional version for [[higher Chern-Simons theory|higher abelian CS theory]] on an oriented smooth manifold of dimension $4n+3$ with boundary a [[complex manifold]] of complex dimension $2n+1$. The talk is expository, and it can be redirected according to the audience's interests and requests.

\linebreak

* {#WilsonApr2023} 26 Apr 2023

  [[Jenny Wilson]] (University of Michigan, USA):

  **Stability patterns for braid groups and configuration spaces**

  cf.: [arXiv:2201.04096](https://arxiv.org/abs/2201.04096)

  slides: [[Wilson-CQTS-Apr-2023.pdf:file]]

  video: [YT](https://www.youtube.com/watch?v=uO2CFY7h5lo)

  > This talk will give an introduction of the field of '[[representation stability]]'. I will discuss how we can use [[representation theory]] to illuminate the structure of certain families of [[groups]] or [[topological spaces]] with [[group action|actions]] of the [[symmetric groups]], focusing on [[braid groups]] and [[configuration spaces of points|configuration spaces]] as motivating examples.

\linebreak

### May 2023

* {#RovelliMay2023} 3 May 2023

  [[Martina Rovelli]] (University of Massachusetts, Amherst, USA):

  **$n$-Complicial sets as a model for $(\infty,n)$-categories**

  cf.: [arXiv:1809.10621](https://arxiv.org/abs/1809.10621), [arXiv:2206.02689](https://arxiv.org/abs/2206.02689)

  video: [YT](https://www.youtube.com/watch?v=T9Bg1AdaKv8)

  > The formalism of [[extended TQFTs]] relies the notion of an [[(infinity,n)-category|$(\infty,n)$-category]]: a categorical structure with [[n-morphism|morphisms in each dimension]], which can be composed in a weakly associative way, and which are weakly invertible in dimension higher than $n$. In this expository talk I will describe the notion of an [[n-complicial sets|$n$-complicial set]], explain the intuition for how this implements the idea of an [[(infinity,n)-category|$(\infty,n)$-category]], and discuss some of the advantages and disadvantages of this approach.

\linebreak

* {#RidoutMay2023} 10 May 2023

  [[David Ridout]]  (University of Melbourne, Australia):

  **A (gentle) introduction to logarithmic conformal field theory**

  > [[conformal field theory|Conformal field theory]] is an integral part of modern [[mathematical physics]] with applications to [[statistical physics]], [[string theory]] and pure [[mathematics]].  Textbooks teach us that such theories are built from [[chiral algebras]] (also called [[vertex operator algebras]]) with nice ([[semisimple category|semisimple]]) [[representation theories]].  But, what happens when the algebra has non-semisimple representations?  This is the defining feature of [[logarithmic conformal field theory]]...

\linebreak

### Sep 2023

* {#YamashitaSep2023} 13 Sep 2023

  [[Mayuko Yamashita]]  (Kyoto University, Japan):

  **Topological Modular Forms and Heterotic String Theory**

  cf. [arXiv:2305.06196](https://arxiv.org/abs/2305.06196), [arXiv:2108.13542](https://arxiv.org/abs/2108.13542)

  > video: [Zm](https://nyu.zoom.us/rec/play/-h0SvD8ppAUvJ0zLbko2tUaGWyEK6O3OSNTtUfCBC2L74t4KyphBnpxTz8Wms1jNfKjXj3LlJB8vs-n8.-r0ZCtHR_F__Xa6w?canPlayFromShare=true)

  > In this talk, I will explain my works with [[Yuji Tachikawa|Y. Tachikawa]] to study [[quantum anomaly|anomalies]] in [[heterotic string theory]] via [[homotopy theory]], especially the theory of [[topological modular forms|Topological Modular Forms]] ([[TMF]]). TMF is an [[E-infinity ring|E-infinity]] [[ring spectrum]] which is [[What is an elliptic object?|conjectured by Stolz-Teichner]] to classify [[(2,1)-dimensional Euclidean field theory|two-dimensional supersymmetric quantum field theories]] in physics. In the previous work [[arXiv:2108.13542](https://arxiv.org/abs/2108.13542)], we proved the vanishing of anomalies in heterotic string theory mathematically using TMF. Additionally, we have a recent update on the previous work [[arXiv:2305.06196](https://arxiv.org/abs/2305.06196)]. Due to the vanishing result, we can consider a secondary transformation of spectra, which coincides with the [[Anderson duality|Anderson self-duality]] morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by [[differential geometry|differential-geometric]] methods.

\linebreak

* {#PennigSep2023} 20 Sep 2023

  [[Ulrich Pennig]] (Cardiff University):

  **Equivariant Higher Twisted K-Theory of $SU(n)$ via Exponential Functors**

  video: [YT](https://youtu.be/JXO-owcJgTE), [Zm](https://nyu.zoom.us/rec/share/lQBkCKp9_n42Fr37HrY_NFMRrjTP3yt2OWdgM7Cs6au3OEwMJoYAinfuGXv6QAYC.a5_q3vxr2KDylHX5)

  cf. [arXiv:2307.00423](https://arxiv.org/abs/2307.00423)

  >  [[twisted K-theory|Twisted K-theory]] is a variant of [[topological K-theory]] that allows [[local coefficient bundle|local coefficient systems]] called [[twisted cohomology|twists]]. For spaces and twists equipped with an [[group action|action]] by a [[group]], [[equivariant twisted K-theory]] provides an even finer invariant. Equivariant twists over [[Lie groups]] gained increasing importance in the subject due to a [[Loop Groups and Twisted K-Theory|result by Freed, Hopkins and Teleman]] that relates the corresponding K-groups to the [[Verlinde ring]] of the associated [[loop group]]. From the point of view of [[homotopy theory]] only a small [[subgroup]] of all possible twists is considered in classical treatments of [[twisted K-theory]]. In this talk I will discuss an operator-algebraic model for equivariant higher (i.e. non-classical) twists over $SU(n)$ induced by exponential functors on the category of vector spaces and isomorphisms. These twists are represented by [[Fell bundles]] and the [[C*-algebra|C*-algebraic]] picture allows a full computation of the associated K-groups at least in low dimensions. I will also draw some parallels of our results with the [[Loop Groups and Twisted K-Theory|FHT theorem]]. This is joint work with [[David E. Evans|D. Evans]].

\linebreak

* 27 Sep 2023

  [[Urs Schreiber]] (NYUAD, CQTS)

  **Quantum Channels as QuantumState Monad Transformations (Part II)**

  notes: [here](https://ncatlab.org/schreiber/show/Quantum+Certification+via+Linear+Homotopy+Types#draft)

  video: [Zm](https://nyu.zoom.us/rec/share/5SJv_CnPhlOwZ6owgjJC7ZUk410y6qLLJoIyrE7WL1O2zZdB8zA1fuvOIUKTbUD5.PoR6XLJamw_FAdoL)

  > The talk recalls some of the theory of "[[quantum channels]]" and then explains how this is captured by "[[monad (in computer science)|monadic computation]]" with the [[linear logic|linear version]] of the "[[state monad|State monad]]" -- the "[[quantum state monad|QuantumState Frobenius monad]]".

\linebreak

### Oct 2023

* {#GiotopoulosOct2023} 4 Oct 2023

  [[Grigorios Giotopoulos]] (NYUAD)

  **Classical field theory in the topos of smooth sets**

  cf. *[[schreiber:Smooth Sets of Fields|Smooth Sets of Fields]]*, [arXiv:2312.16301](https://arxiv.org/abs/2312.16301)

  notes: [[Giotopoulos-FieldTheoryInSmoothSets.pdf:file]]

  video: [YT](https://youtu.be/7Bw9CJct8QY), [Zm](https://nyu.zoom.us/rec/share/nqJEvc4n9dXoyRiou4s-t0Fp5W4bGKma6GDfzZtk1Es9llYJocNMFbxHzV9iSd55.-c3wp3VzQ5WlbdH3)

  > By recalling the textbook description of a ([[variational calculus|variational]]) [[classical field theory]] and its [[critical locus]] of [[on-shell]] [[field (physics)|fields]], I will list desiderata for a [[category]] in which this can rigorously take place. This category will consist of [[generalized smooth spaces]], completely determined by "how they may be smoothly probed by finite dimensional manifolds". By expanding on this intuition, I will describe how one naturally arrives at the definition of a [[smooth set]] as a "[[sheaf]] over the [[site]] [[CartSp|of]] [[Cartesian spaces]]''. I will then explain how the [[sheaf topos]] of [[smooth sets]] satisfies the desiderata of (variational) classical field theory. Time permitting, I will indicate how the setting naturally generalizes to include the description of [[fermionic fields]], and ([[gauge field|gauge]]) fields with [[internal symmetries]].

\linebreak

* {#OkayOct2023} 11 Oct 2023

  [[Cihan Okay]] (Bikent University):

  **Simplicial Distributions and Contextuality**

  video: [YT](https://youtu.be/pgKYGUWl1kU), [Zm](https://nyu.zoom.us/rec/share/eCYVcE8H1awJQBiz_KO8tFKiSzg6z7fuNOezzMRtwMmDhBfvYggd6gsQzpMCHdhz.P2-aYYVnZnxYJbR-)

  cf. [arXiv:2204.06648](quantum+contextuality#OkayKharoofIpek22)

  >  In modern [[homotopy theory]], spaces are represented by combinatorial models called [[simplicial sets]]. Their elegant formulation gives them great expressive power to capture spaces up to homotopy. Simplicial distributions are basic mathematical objects that mix simplicial sets with [[probability|probabilities]]. That is, they model probability distributions on spaces. In my talk, I will show how simplicial distributions provide a framework for studying a central quantum feature associated with probabilities, known as [[quantum contextuality|contextuality]]. A typical [[quantum measurement|measurement]] scenario consists of a set of measurements and outcomes, whereas simplicial distributions can be defined for spaces of measurements and outcomes. Our approach unifies and goes beyond two earlier approaches: the sheaf-theoretic ([Abramsky-Brandenburger](quantum+contextuality#AbramskyBrandenburger11)) and group cohomological ([Okay-Roberts-Bartlett-Raussendorf](quantum+contextuality#OkayRobertsBartlettRaussendorf17)).

\linebreak

* {#KapulkinOct2023} 18 Oct 2023

  [[Chris Kapulkin]] (Western University, Canada):

  **Calculus of Fractions for Quasicategories** (Part I)

  video: [YT](https://youtu.be/96ViSKAuApc), [Zm](https://nyu.zoom.us/rec/share/POx38qJ4lpNVexajPFMmHLE2sWFGb7IZhLBcbHpqAcDEWUg1SEjDG8hMOGD2dKPM.QAZR-7Rv4FXcD7v8)

  cf.: [arXiv:2306.02218](https://arxiv.org/abs/2306.02218)

  > In their 1967 book "[[Calculus of Fractions and Homotopy Theory]]", [[Pierre Gabriel|P. Gabriel]] and [[Michel Zisman|M. Zisman]] introduced *[[calculus of fractions]]* as a tool for understanding the [[localization of a category]] at a class of [[weak equivalences]]. While powerful, the condition of calculus of fractions is quite restrictive and it is rarely satisfied in various [[homotopy theory|homotopical]] settings, like [[model categories]] or [[Kenneth Brown|Brown]]'s [[categories of fibrant objects]], where one instead has homotopy calculus of fractions. This talk is based on a recent preprint [arXiv:2306.02218](https://arxiv.org/abs/2306.02218), which aims to reconcile the two. We define [[calculus of fractions]] for [[quasicategories]] and give a workable model for [[marked simplicial set|marked]] quasicategories satisfying our condition. Although we have already found several applications of this result, we would be very interested in getting feedback from the audience and exploring new applications from diverse areas.

\linebreak

* {#CarranzaOct2023} 25 Oct 2023

  [[Daniel Carranza]] (Western University, Canada):

  **Calculus of Fractions for Quasicategories (Part II)**

  video: [YT](https://youtu.be/Z41YDb99cZk), [Zm](https://nyu.zoom.us/rec/share/sBTbtlBMEU3QdKN5SYEytwXlt5zo10a2N7-KK9ekfx2h0WVtYlH2e53mYRpH1TkU.CTXtj25re0wLSjoV)

  cf.: [arXiv:2306.02218](https://arxiv.org/abs/2306.02218)

  > In their 1967 book "[[Calculus of Fractions and Homotopy Theory]]", [[Pierre Gabriel|P. Gabriel]] and [[Michel Zisman|M. Zisman]] introduced *[[calculus of fractions]]* as a tool for understanding the [[localization of a category]] at a class of [[weak equivalences]]. While powerful, the condition of calculus of fractions is quite restrictive and it is rarely satisfied in various [[homotopy theory|homotopical]] settings, like [[model categories]] or [[Kenneth Brown|Brown]]'s [[categories of fibrant objects]], where one instead has homotopy calculus of fractions. This talk is based on a recent preprint [arXiv:2306.02218](https://arxiv.org/abs/2306.02218), which aims to reconcile the two. We define [[calculus of fractions]] for [[quasicategories]] and give a workable model for [[marked simplicial set|marked]] quasicategories satisfying our condition. Although we have already found several applications of this result, we would be very interested in getting feedback from the audience and exploring new applications from diverse areas.

\linebreak

### Nov 2023

* {#WangNov23} 01 Nov 2023

  [[Juven Wang]] (Harvard University):

  **Ultra Unification, and Noninvertible Symmetry of the Standard Model from Gravitational Anomaly**

  cf.: [arXiv:2012.15860](topological+phase+of+matter#Wang21), [arXiv:arXiv:2302.14862](generalized+global+symmetry#PutrovWang23)

  video: [Zm](https://nyu.zoom.us/rec/share/y18MXMK329GQKDyQI-lrCHDk_nH7RPXxwSZjDH5Xt2fCnlpzvJln6zFwcvcFMxyB.oLZSTWyVv4pNKk3h)

  > In the [[standard model of particle physics|Standard Model]], the total "[[sterile neutrino|sterile right-handed]]" [[neutrino]] number $n_{vR}$ is not equal to the family number $N_f$. The anomaly index $(-N_f + n_{vR})$ had been advocated to play an important role in the previous work on *Cobordism and Deformation Class of the Standard Model* [[arxiv:2112.14765](https://arxiv.org/abs/2112.14765), [arxiv:2204.08393](https://arxiv.org/abs/2204.08393)] and *Ultra Unification* [[arXiv:2012.15860](https://arxiv.org/abs/2012.15860)], in order to predict new highly [[quantum entanglement|entangled]] sectors beyond the Standard Model. Ultra Unification would combine the Standard Model and [[GUT|Grand Unification]], particularly for the models with 15 [[Weyl spinor|Weyl fermions]] per family, without the necessity of [[sterile neutrino|right-handed sterile neutrinos]], by adding new gapped [[topological phase of matter|topological phase]] sectors (in 4d or 5d) or new gapless interacting [[conformal field theory|conformal]] sectors (in 4d) consistent with the [[nonperturbative effect|nonperturbative]] global [[anomaly cancellation]] and cobordism constraints (especially from the mixed gauge-gravitational anomaly, such as a $\mathbb{Z}_{16}$ class anomaly, associated with the baryon minus [[lepton]] number B−L and the [[electroweak field|electroweak]] [[hypercharge]] $Y$). Moreover, for the Standard Mode alone, the invertible B−L symmetry [[conserved charge|current]] conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons, hypothetically pertinent for [[leptogenesis]] in the very early [[observable universe|universe]]. In specific, we show that a [[generalized global symmetry|noninvertible categorical]] counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we construct noninvertible symmetry charge operators as topological [[defect field theory|defects]] derived from invertible anomalous symmetries that suffer from mixed [[gravitational anomalies]]. Examples include the perturbative local and nonperturbative global anomalies classified by $\mathbb{Z}$ and $\mathbb{Z}_{16}$ respectively. For this construction, we utilize the [[anomaly inflow]] concept, the 4d [[Pontryagin class]] and the gravitational [[Chern-Simons form|Chern-Simons 3-form]], the 3d [[Reshetikhin-Turaev construction|Witten-Reshetikhin-Turaev-type]] [[topological quantum field theory]] with a framing anomaly corresponding to a 2d [[rational conformal field theory]] with an appropriate chiral [[central charge]], and the 4d $\mathbb{Z}_4$^{TF}-[[time-reversal symmetry|time-reversal symmetric]] [[topological superconductor]] with 3d boundary topological order [[arxiv:2302.14862](https://arxiv.org/abs/2302.14862)].

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* {#JohnsonFreydNov2023} 08 Nov 2023

  [[Theo Johnson-Freyd]] (Dalhousie University):

  **Higher Dagger Categories**

  slides: [pdf](http://categorified.net/NYUADtalk.pdf)

  video: [YT](https://youtu.be/zvtziTpl2T0), [Zm](https://nyu.zoom.us/rec/share/Q7Ty3uC2Zeiu39sVmZvYh25NavFZn36vWGpjYTzAwRYRS_d4ZWSKQeY3neFMgVxB.c6yUMNTsLexdXnTA)

  cf. [categorified.net/dagger2023.html](http://categorified.net/dagger2023.html)

  > [[Hilbert spaces]] form more than a category: their morphisms maps can be composed, but also every morphism $f : X \to Y$ has a distinguished "[[adjoint operator|adjoint]]" $f^\dagger : Y \to X$, making it into a "[[dagger category]]". This extra data is important for axiomatizing [[functional analysis]], [[quantum mechanics]], [[quantum information theory]]... However, the assignment $f \mapsto f^\dagger$ is unsatisfying from a [[higher category theory|higher category theorist]]'s perspective because it is "evil", i.e. it violates the [[principle of equivalence]]: a category [[equivalence of categories|equivalent]] to a [[dagger category]] may not admit a dagger structure. This in particular interferes with generalizing the notion of dagger category to the (non-strict) [[higher categories]] necessary for axiomatizing [[extended field theory|fully-local quantum field theory]]. In this talk I will propose a manifestly non-evil definition of "dagger $(\infty,n)$-category". The same machinery also produce a non-evil definitions of "pivotal $(\infty,n)$-category" and helps to clarify the relationship between [[reflection positivity]] and [[spin-statistics theorem|spin-statistics]]. This is based on joint work with [[Bruce Bartlett|B. Bartlett]], G. Ferrar, B. Hungar, C. Krulewski, [[Lukas Müller|L. Müller]], N. Nivedita, [[David Penneys|D. Penneys]], [[David Reutter|D. Reutter]], [[Claudia Scheimbauer|C. Scheimbauer]], [[Luuk Stehouwer|L. Stehouwer]], and C. Vuppulury.

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* {#DornNov2023} 15 Nov 2023

  [[Christoph Dorn]] (Oxford University):

  **Manifold Diagrams -- A Brief Report**

  slides: [[Dorn-ManifoldDiagramsReport.pdf:file]]

  video: [YT](https://youtu.be/7KK89MuxmX8), [Zm](https://nyu.zoom.us/rec/share/pqfp60d108XRrenD5M1hOnwHiknUmargmTIHwZZUU_Ou4zLhV92a2LZFW0tdYUFQ.y2DKUvtBPKLbGWlL)

  cf.: [arXiv:2208.13758](https://arxiv.org/abs/2208.13758)

  > [[manifold diagram|Manifold diagrams]] are the [[higher category|higher]] [[categorifications]] of [[string diagrams]]. They lie at the intersection of several interesting topics, such as: 1. The [[tangle hypothesis|tangle]] and [[cobordism hypotheses]], 2. The constructive description of [[computads|free higher categorical structures]], 3. The combinatorialization of differential structures and [singularities](cobordism+hypothesis#ForCobordismsWithSingularities). Nonetheless, the precise role of manifold diagrams in these topics remains largely mysterious. In this talk, we will focus on describing the basic interplay between ([[stratified space|stratified]]) geometry, [[combinatorics]], and (directed) cell complexes, exposed by the mathematical framework of manifold diagrams. This will include, in particular, two equivalent definitions of manifold diagrams, one geometric and one combinatorial, as well as a discussion of how these relate to the above topics

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* {#CattaneoNov2023} 22 Nov 2023

  [[Alberto Cattaneo]] (Zurich University, Switzerland):

  **Poisson Structures from Corners of Field Theories**

  slides: [[Cattaneo-PoissonStrucFromCorners.pdf:file]]

  video: [YT](https://youtu.be/_bGH09FmAxk), [Zm](https://nyu.zoom.us/rec/share/cvJN1WxKAy90-TU2xGGgI_qpr29cXwYnViJK2f7sicBsvZoOfAxYS1oHAURPgtbn.r4soFI_hw6c9Wtok)

  cf. [arXiv:2310.01877](first-order+formulation+of+gravity#CattaneoMengerSchiavina23)

  > The [[BV formalism]] and its [[shifted symplectic structure|shifted]] versions in [[field theory]] have a nice compatibility with [[boundary field theory|boundary]] structures. Namely, one such structure in the [[bulk]] induces a shifted (possibly degenerated) version on its boundary, which can be interpreted as a [[Poisson structure]] ([[Poisson n-algebra|up to homotopy]]). I will present the results for some field theories, in particular, 4D [[BF theory]] and [[Einstein gravity|4D gravity]].

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### Dec 2023

* {#TorzewskaDec2023} 06 Dec 2023

  [[Fiona Torzewska]] (University of Leeds, UK):

  **Topological Quantum Field Theories and Homotopy Cobordisms**

  slides: [[Torzewska-TQFTandHomCob.pdf:file]]

  video: [YT](https://youtu.be/7rtJ61EPL-M)

  cf: [arXiv:2208.14504](TQFT#Torzewska22)

  > I will begin by explaining the construction of a [[category]] $CofCos$, whose [[objects]] are [[topological spaces]] and whose [[morphisms]] are [[cofibrant object|cofibrant]] [[cospans]]. Here the [[identity morphism|identity]] [[cospan]] is chosen to be of the form $X\to X\times [0,1]\rightarrow X$, in contrast with the usual identity in the [[bicategory]] $Cosp(V)$ of cospans over a category $V$. The category $CofCos$ has a [[subcategory]] $HomCob$ in which all spaces are homotopically 1-finitely generated. There exist [[functors]] into $HomCob$ from a number of categorical constructions which are potentially of use for modelling [[particle]] [[trajectories]] in [[topological phases of matter]]: embedded cobordism categories and [motion groupoids](motion+groupoid#TorzewskaMartinsMartin23) for example. Thus, functors from $HomCob$ into [[Vect]] give [[linear representation|representations]] of the aforementioned categories. I will also construct a family of [[functors]] $Z_G\colon HomCob\to Vect$, one for each [[finite group]] $G$, and show that [[topological quantum field theories]] previously constructed [[Yetter model|by Yetter]], and an untwisted version of [[Dijkgraaf-Witten theory|Dijkgraaf-Witten]], generalise to functors from $HomCob$. I will construct this functor in such a way that it is clear the [[images]] are [[finite dimensional vector spaces]], and the functor is explicitly calculable. I will also give example calculations throughout.

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* {#MayDec2023} 13 Dec 2023

  [[Clover May]] (Norwegian University of Science and Technology):

  **Classifying Modules of Equivariant Eilenberg–MacLane Spectra**

  cf.: [arXiv:2203.05287](Bredon+cohomology#DuggerHazelMay24)

  > Classically, since $\mathbb{Z}/p$ [[prime field|is a field]], any [[module spectrum|module]] over the [[Eilenberg-MacLane spectrum]] $H \mathbb{Z}/p$ splits as a [[wedge sum|wedge]] of [[reduced suspension|suspensions]] of $H \mathbb{Z}/p$ itself. Equivariantly, the module theory of [[equivariant stable homotopy theory|$G$-equivariant]] Eilenberg—MacLane spectra is much more complicated.  For the [[cyclic group]] $G=C_p$ and the [[constant functor|constant]] [[Mackey functor]] $\mathbb{Z}/p$, there are infinitely many [[indecomposable object|indecomposable]] $H \mathbb{Z}/p$-modules. [Previous work](Bredon+cohomology#DuggerHazelMay24) together with [[Daniel Dugger|Dugger]] and [[Christy Hazel|Hazel]] classified all indecomposable $H \mathbb{Z}/2$-modules for the group $G=C_2$. The [[isomorphism classes]] of indecomposables fit into just three families. By contrast, we show for $G=C_p$ with $p$ an [[odd number|odd]] [[prime number|prime]], the classification of indecomposable $H \mathbb{Z}/p$-modules is wild. This is joint work in progress with Grevstad.

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### Jan 2024

* 24 Jan 2024:

  Quentin Ehret:

  **Central extensions of restricted Lie superalgebras and classification of $p$-nilpotent Lie superalgebras in dimension 4**

  cf.: [arXiv:2401.08313](https://arxiv.org/abs/2401.08313)

  > [[ground field|Over a field]] of [[positive characteristic]] $p$, restricted [[Lie algebras]] are of prime interest, mainly due to their link to [[algebraic groups]] and their role in [[representation theory]] and classification. The [[Lie algebra cohomology|cohomology]] associated with restricted Lie algebras is considerably more complicated than the ordinary [[Chevalley-Eilenberg complex|Chevalley-Eilenberg cohomology]] and explicit formulas are only known up to order 2. In this talk, I will explain how to build the first and second restricted cohomology groups for restricted [[Lie superalgebras]] in [[characteristic]] $p$ greater than 3, modifying a previous construction.  I will explain how these groups capture some algebraic structures, such as restricted extensions.  Further, I will show how to apply this construction to classify $p$-nilpotent restricted Lie superalgebras up to dimension 4 over an [[algebraically closed field]] of characteristic $p$ greater than 3. This is a joint work with Sofiane Bouarroudj (NYU Abu Dhabi).

\linebreak

* 31 Jan 2024

  [[Chris Blair]]:

  **Geometry and Dualities of Decoupling Limits in String Theory and M-Theory**

  cf.: [arXiv:2311.10564](https://arxiv.org/abs/2311.10564)

  > Our understanding of [[M-theory]] is based on a [[duality in string theory|duality web]] connecting different limits of the theory. I'll discuss the extension of this duality web to a wide variety of decoupling limits related by duality to the null reduction of M-theory (and hence to the proposal that M-theory can be described by [[BFSS matrix model|Matrix theory]]). From a modern perspective, these limits involve non-[[relativistic field theory|relativistic]] geometries, leading to new variants of [[supergravity]] in [[D=11 supergravity|11-]] and [[D=10 supergravity|10-dimensions]]. I'll discuss how to systematically explore these corners of M-theory, following the roadmap of [arxiv.org/abs/2311.10564](https://arxiv.org/abs/2311.10564).

\linebreak

### Feb 2024

* {#ChenFeb2024} 07 Feb 2024

  [[Hank Chen]] (University of Waterloo, Canada):

  **Higher Anomaly Resolution from $L_\infty$ Algebras**

  > This talk is based on [arXiv:2211.08549](Dirac+monopole#ChenGirelli22), in which we explore the [[higher Lie theory|Lie higher-algebraic]] and [[higher geometry|higher-geometric]] structures that arise from a procedure we dub "gauging the gauge", and study the resulting [[higher gauge theory|2- and 3-gauge theory]]. The homotopy weakening of algebraic properties afforded by [[Lie n-algebra|Lie $L_n$-algebras]] is tied to violation of geometric higher-[[Bianchi identity|Bianchi conditions]]. In this talk, I will focus on the application of this observation to two specific cases, and examine its consequences. First, for the [[monopole]] [[circle group|$U(1)$]] gauge theory, the above observation gives rise to the [[2-group]] [[Green-Schwarz anomaly cancellation]] ([Benini-Cordova-Intriligator 2019](Green-Schwarz+mechanism#BeniniCordovaHsin19)), and the associated dipole conservation laws exhibit mobility restriction akin to fractonic matter (Slagel-Kim 2017). Second, for the [[string 2-group|string 2-gauge]] theory, we find a [[3-group]] worth of charges exhibiting novel and intricate mobility restrictions and, under certain assumptions, the resulting 3-gauge theory achieves a higher-monopole charge which matched the [[first fractional Pontrjagin class|fractional Pontrjagyn class]] $\tfrac{1}{2}p_1$. This gives a way in which the [[string structure]] of a [[spin manifold]] $X$ can be probed dynamically by a 3-group gauge theory.

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* {#HaghighatFeb2024} 14 Feb 2024

  [[Babak Haghighat]] (Tsinghua University, China):

  **Flat Connections from Irregular Conformal Blocks**

  cf. [arXiv:2311.13358](https://arxiv.org/abs/2311.13358), [arXiv:2311.07960](https://arxiv.org/abs/2311.07960)

  >  I will talk about [[Liouville theory|Liouville]] [[conformal blocks]] with degenerate primaries and one operator in an irregular representation of the [[Virasoro algebra]]. Using an algebraic approach, we derive modified BPZ equations satisfied by such blocks and subsequently construct corresponding integral representations based on integration over non-compact Lefschetz cycles. The integral representations are then used to derive novel types of [[flat connections]] on the irregular conformal block bundle.

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## External presentations
 {#ExternalTalk}

External presentations reporting on work at CQTS.

\linebreak

### Sep 2022

* 15 Sep 2022 at *[PlanQC 2022](https://icfp22.sigplan.org/home/planqc-2022)*

  [[Urs Schreiber]] on joint work with [[Hisham Sati]]:

  **[[schreiber:Topological Quantum Programming in TED-K]]**

  slides: [pdf](https://ncatlab.org/schreiber/files/TQCinTEDK-PlanQC-220905b.pdf) (view full screen)

  * video: [YT](https://www.youtube.com/watch?v=hDwXQVcloB8&feature=emb_logo)

  * extended abstract: [arXiv:2209.08331](https://arxiv.org/abs/2209.08331)

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* {#MathFacultyMeetingSep2022} 16 Sep 2022 at *Math Faculty Meeting*, NYU Abu Dhabi

  [[Urs Schreiber]] on joint work with [[Hisham Sati]]:

  **Practical Foundations for Topological Quantum Programming**

  slides: [[TQPFoundations-MathFacultyMeeting-20220916.pdf:file]]

\linebreak

### Nov 2022

* {#QTML22} 12 Nov 2022 at *[Workshop on Quantum Software](https://quasar.unina.it/qtml2022/workshop.php)*, satellite of *[QTML 2022](https://quasar.unina.it/qtml2022.html)* (Naples, Italy)

  [[Urs Schreiber]] on joint work with [[nLab:David Jaz Myers|D. J. Myers]], [[nLab:Mitchell Riley|M. Riley]] and [[nLab:Hisham Sati|H. Sati]]:

  **[Quantum Data Types via Linear Homotopy Type Theory](https://ncatlab.org/schreiber/show/QDataInLHoTT#QTML2022)**

  slides: [pdf](https://ncatlab.org/schreiber/files/QuantumDataInLHoTT-221112f.pdf)

  > The proper concept of [[nLab:data types]] in [[nLab:quantum programming languages]], hence of their [[nLab:certified programming|formal verification]] and [[nLab:categorical semantics]], has remained somewhat elusive, as witnessed by the issue of "[dynamic lifting](https://ncatlab.org/nlab/show/Quipper#ReferencesDynamicLifting)" encountered in the [[nLab:Quipper]] language family. In this talk I explain our claim that a powerful [[nLab:quantum computation|quantum]] [[nLab:data type]]-system elegantly solving these problems is naturally provided by the *[[nLab:linear homotopy type theory]]* recently [realized](https://ncatlab.org/nlab/show/dependent+linear+type+theory#Riley22) by [[nLab:Mitchell Riley|M. Riley]]. Together with our [previous claim](Topological+Quantum+Programming+in+TED-K#GMConAbs) that [[nLab:homotopy type theory]] natively knows about the fine detail of [[nLab:su(2)-anyon|$\mathfrak{su}$(2)-]][[nlab:anyon]] [[nLab:braid representation|braid]] [[nLab:quantum gates]], this shows that [[nLab:linear homotopy type theory]] is a natural substrate for [[nLab:type theory|typed]] [[nLab:quantum programming languages]] aware of [[nLab:topological phases of matter|topological]] [[nLab:quantum materials|quantum hardware]].

\linebreak

### Dec 2022

* {#ValeraDec2020} 17 Dec 2022 at [AQIS 2022](http://aqis-conf.org/2022/)

  [[Sachin Valera]]:

  **Braidless Topological Quantum Teleportation**

  poster: [[Valera-BraidlessTopologicalQT-230127.pdf:file]]

  > on [[quantum teleportation]] with/of [[anyons]]

\linebreak

### Jan 2023

\linebreak

* 15 Jan 2023

  [[Hisham Sati]]:

  **M-theory and matter via Twisted Equivariant Differential (TED) K-theory**

  talk at *[M-Theory and Mathematics 2023](/nlab/show/M-Theory+and+Mathematics#2023)*, NYU Abu Dhabi

  [[links](/nlab/show/M-Theory+and+Mathematics#Sati2023)]

\linebreak

* 15 Jan 2023

  [[Urs Schreiber]]:

  **[[schreiber:Topological Quantum Gates from M-Theory]]**

  talk at *[M-Theory and Mathematics 2023](/nlab/show/M-Theory+and+Mathematics#2023)*, NYU Abu Dhabi

  [[links](/nlab/show/M-Theory+and+Mathematics#Schreiber2023)]

\linebreak

### Feb 2023

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    "width": 180,
    "unit": "px",
    "float": "right",
    "margin": {
        "top": -60,
        "bottom": 20,
        "right": 20,
        "left": 50
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\end{imagefromfile}

\linebreak

* {#JavedFeb2023} 20 Feb 2023

  [[Amaria Javed]]:

  **Simulating an all-optical quantum controlled-NOT gate using soliton scattering by a reflectionless potential well**

  talk at *[UAE U Nonlinear Physics Group Conference](https://ncatlab.org/nlab/files/UAEU-Non%20LinPhyGrpConf2023-Program.pdf)*, Al Ain

\linebreak

### Mar 2023

> [[Asif Equbal]] (far left) and [[Amaria Javed]] (far right)

\linebreak

### Apr 2023

* {#MyersApr2023} 10 Apr 2023

  [[David Jaz Myers]]:

  **How do you identify one thing with another? -- an intro to Homotopy Type Theory**

  talk at Prof. [[Sadok Kallel]]'s colloquium,

  American University of Sharjah

  slides: [[Myers-IntroHoTT-Apr2023.pdf:file]]

\linebreak

* [13 April 2023](https://researchseminars.org/talk/ToposInstituteColloquium/87/)

  [[Urs Schreiber]]:

  **[[schreiber:Quantum Certification via Linear Homotopy Types|Effective Quantum Certification via Linear Homotopy Types]] --- Part I**

  [talk at](https://researchseminars.org/talk/ToposInstituteColloquium/87/) [Colloquium of the *Topos Institute*](https://topos.site/topos-colloquium/)

  slides: [pdf](https://ncatlab.org/schreiber/files/Schreiber-ToposInstitute-230413b.pdf) (view full screen)

  video: [YT](https://www.youtube.com/watch?v=G24jHsx_BQE)

\linebreak

### Aug 2023

* [24 Aug 2023](https://researchseminars.org/talk/ToposInstituteColloquium/104/)

  [[Urs Schreiber]]:

  **[[schreiber:Quantum Certification via Linear Homotopy Types|Effective Quantum Certification via Linear Homotopy Types]] --- Part II**

  [talk at](https://researchseminars.org/talk/ToposInstituteColloquium/104/) [Colloquium of the *Topos Institute*](https://topos.site/topos-colloquium/)

  slides: [pdf](https://ncatlab.org/schreiber/files/Schreiber-ToposInstitute-230413b.pdf) (view full screen)

  video: [YT](https://www.youtube.com/watch?v=tqsH41b2xFA)

\linebreak

### Feb 2024

* 02 Feb 2024

  [[Urs Schreiber]]:

  **[Topological Quantum Programming with Linear Homotopy Types](/schreiber/show/Topological+Quantum+Gates+in+Homotopy+Type+Theory#HoTTEST2024)**

  talk at: *[Homotopy Type Theory Electronic Seminar,](https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html)*,

  video: [YT](https://youtu.be/Wnm3yCUzNb0)

\linebreak

***

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## Members
 {#Members}

Principal Investigator:

* [[Hisham Sati]]

co-PIS:

* [[Tim Byrnes]]

* [[Asif Equbal]]

* [[Muhammad Shafique]]

* for more see [here](https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/center-for-quantum-and-topological-systems.html)

Senior Researcher:

* [[Urs Schreiber]]

Researchers:

* [[Adrian Clough]]

* [Tatiana Ezubova](https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts/researchers/tatiana-ezubova.html)

* [[Grigorios Giotopoulos]]

* [[Amaria Javed]]

* [[Marwa Mannaï]]

* [[David Jaz Myers]]

* [[Mitchell Riley]]

* [[Vivek Kumar Singh]]

* [[Sachin Valera]]

***

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[[!redirects CQTS]]

category: reference