bluuebunny/crossref_metadata_2025_split huggingface dataset:
Arakelov Geometry
Authors: Bost Jean-Benoît , Künnemann Klaus , Roessler Damian 
Published: December 2009

Arakelov geometry studies the geometry and arithmetic of schemes of finite type over Spec

{\bf Z}

, i.e. systems of polynomial equations with integer coefficients. It combines methods from algebraic geometry, number theory, and hermitian differential geometry.

The workshop was organized by Jean-Benoît Bost (Orsay), Klaus Künnemann (Regensburg) and Damian Roessler (Paris). It brought together internationally leading experts in the area as well as a considerable number of young researchers. The talks covered various aspects of Arakelov geometry from analytic torsion over adelic and non-archimedean analytic spaces to modular forms and diophantine geometry.
A non-mathematical complement was a piano recital by Harry Tamvakis on Thursday night featuring Bach, Beethoven and Chopin.
Deformations and Contractions in Mathematics and Physics
Authors: Fialowski Alice , Novikov Sergey , Schlichenmaier Martin , de Montigny Marc 
Published: December 2009

Deformations of mathematical structures are not only important in most parts of mathematics but also to a large extend in physics. Contractions are in some respect dual to deformations. The aim of the proposed workshop was to bring together world experts in these complementary topics of deformations and contractions of various algebraic structures. Deformations and contractions have been investigated by researchers who had different approaches and goals. Tools such as cohomology, gradings, etc. which are utilized in the study of one concept, are likely to be useful for the other concept as well. At this meeting there were mathematicians, mathematical physicists and physicists as well. The organizers hope that the meeting was of benefit to all groups.
Because various fields in mathematics and physics exist in which deformations are used, it was necessary to focus the topic of the workshop. The meeting mainly considered deformations of algebras (in particular, of Lie algebras), groups, and related algebraic structures, the corresponding contractions, and their applications to problems in physics. Nevertheless, other fields with strong relations to the central topic were present too. One such field, discussed in detail at the workshop, with tight interaction was deformation quantization. But also other topics like quantum groups, deformation of Hopf algebras, q-deformed physics, fuzzy spaces, quantum systems as deformations of classical systems, etc showed up.
As the workshop had an interdisciplinary character it was considered to be useful to start with some introductory talks on
with the aim to introduce the necessary concepts which were not always well known to all the different communities present. For more details on the concepts, see the corresponding extended abstracts in this Oberwolfach report.
The following is a (non-exhaustive) list of topics which were discussed at the workshop.
The workshop was attended by 44 participants from all over the world. The official program consisted of 24 lectures. Two evening sessions of informal presentations were organised. Beside the official program, there was ample time for the participants for further activities, such as self-organised sessions and discussion groups.
Algorithmic Graph Theory
Authors: Czumaj Artur , Jansen Klaus , Meyer auf der Heide Friedhelm , Schiermeyer Ingo 
Published: December 2009

The workshop
Algorithmic Graph Theory
, organized by Artur Czumaj (New Jersey), Friedhelm Meyer auf der Heide (Paderborn), Klaus Jansen (Kiel) and Ingo Schiermeyer (Freiberg) was held February 12th–February 18th, 2006. This meeting was attended by 46 participants from a wide range of geographic regions, many of them young researchers. In the morning sessions survey talks providing an overview of recent developments in Algorithmic Graph Theory were presented.

Geometry and Graphs

Graph Algorithms

Game Theory and Graphs

Graph Structures
There were 10 shorter talks and two special sessions on “Graph Algorithms” (organized by Christian Sohler) and “Graph Colourin” (organized by Ingo Schiermeyer). The contributions showed progress in the field provided in recent years. Furthermore, several open problems and conjectures were presented, some of them still far from being resolved. Beyond the program there was plenty of time for the participants to use the stimulating atmosphere of the Oberwolfach Institute for fruitful discussions.
Discrete Differential Geometry
Authors: Bobenko Alexander I. , Kenyon Richard , Sullivan John M. , Ziegler Günter M. 
Published: December 2009

The workshop
Discrete Differential Geometry
, organized by Alexander I. Bobenko (Berlin), Richard W. Kenyon (Vancouver), John M. Sullivan (Berlin) and Günter M. Ziegler (Berlin), was held March 5th to March 11th, 2006. The meeting was very well attended, with almost 50 participants, from as far away as Australia and China.

Discrete differential geometry is a new and active mathematical terrain where differential geometry (providing the classical theory for smooth manifolds) and discrete geometry (concerned with polytopes, simplicial complexes, etc.) meet and interact. Problems of discrete differential geometry also naturally appear in (and are relevant for) other areas of mathematics. Moreover, the process of discretizing notions, problems and methods from the smooth theory often brings out new connections and interrelations between different areas.
The workshop at Oberwolfach brought together researchers with a wide variety of backgrounds, including of course discrete geometry and differential geometry, but also integrable systems, combinatorics, mathematical physics and geometry processing. The exchange of ideas among different subfields helped to build new bridges between these mathematical communities.
Discrete differential geometry can be said to have arisen from the observation that when a notion from smooth geometry (such as the notion of a minimal surface) is discretized “properly”, the discrete objects are not merely approximations of the smooth ones, but have special properties of their own which make them form in some sense a coherent entity by themselves. The discrete theory would seem to be the more fundamental one: The smooth theory can always be recovered as a limit, while there seems to be no natural way to predict from the smooth theory which discretizations will have the nicest properties.
One case where these ideas seem particularly well-developed is for geometries described by integrable systems. The notion of a discrete integrable system as given by consistency on a cubic lattice has already shed new light on classical, smooth integrable systems.
Another theme which arose repeatedly during the workshop was that of circle patterns and sphere packings. These can be used to discretize conformal maps, isothermic surfaces, and elastic bending energy.
Since a computer works with discrete representations of data, it is no surprise that many of the applications of discrete differential geometry are found within computer science, particularly in the areas of computational geometry, graphics and geometry processing. The workshop brought theoreticians together with people interested in these and other applications.
Topological and Geometric Methods in Group Theory
Authors: Bridson Martin R. , Kropholler Peter H. , Vogtmann Karen 
Published: December 2009

The focus of this meeting was the use of topological and geometric methods to study infinite discrete groups. These methods are increasingly being supplemented by powerful new techniques from analysis. Key topics included group actions on CAT(0) and tree-like spaces, filling invariants, cohomology, K-theory and

\ell^2

-cohomology, amenability and Kazhdan's property (T), and deformation spaces, curve complexes and Teichmüller space. More specific information is contained in the abstracts which follow in this volume.

The meeting was organized around a series of 23 lectures each of 50 minutes' duration representing the major recent advances in the area. The first day's lectures were selected from the abstracts and talk proposals which had been submitted in advance of the meeting, and the remainder were decided on Monday and Tuesday morning; in this way were able to take advantage of a full range of abstracts and also to incorporate last-minute information about exciting developments in the field. We had interesting proposals from virtually every participant but lecture slots for fewer than half to speak. We posted all abstracts on the wall of the lecture building and drew attention to them by running a poster event on Tuesday evening, at which every participant took the opportunity to introduce their research and poster. This worked very effectively and was valuable especially to younger people or those visiting the Forschungsinstitut for the first time. It also led to small groups getting together for unofficial lecture sessions in the evening and afternoon breaks on subsequent days.
There were 51 participants from a wide range of countries, including Germany, France, the United States, the United Kingdom, Greece, Russia, Poland, Switzerland and Australia. We are grateful to the European Union, which provided funds to support 6 advanced graduate students, a number of recent Ph. Ds and a few senior researchers.
We feel that the meeting was exciting and highly successful. The quality of the lectures was outstanding, and outside of lectures there was a constant buzz of intense mathematical conversations. One indication of the high degree of current activity and interest in the subject is the fact that four of the participants (including two of the organizers) have been invited to speak at the upcoming International Congress of Mathematicians in Madrid.
Mini-Workshop: The Hauptvermutung for High-Dimensional Manifolds
Authors: Pedersen Erik Kjaer , Ranicki Andrew 
Published: December 2009

The Mini-Workshop
The Hauptvermutung for High-Dimensional Manifolds
, organised by Erik Pedersen (Binghamton) and Andrew Ranicki (Edinburgh) was held August 13th–18th, 2006. The meeting was attended by 17 participants, ranging from graduate students to seasoned veterans.

The manifold Hauptvermutung is the conjecture that topological manifolds have a unique combinatorial structure. This conjecture was disproved in 1969 by Kirby and Siebenmann, who used a mixture of geometric and algebraic methods to classify the combinatorial structures on manifolds of dimension

>4

. However, there is some dissatisfaction in the community with the state of the literature on this topic. This has been voiced most forcefully by Novikov, who has written “In particular, the final Kirby–Siebenmann classification of topological multidimensional manifolds therefore is not proved yet in the literature.” ()

At this conference we discussed a number of questions concerning the Hauptvermutung and the structure theory of high-dimensional topological manifolds. These are our conclusions:

We found nothing fundamentally wrong with the original work of Kirby and Siebenmann [4], which is solidly grounded in the literature. Their determination of

\textit{TOP}/\textit{PL}

depends on Kirby's paper on the Annulus Conjecture and his ‘torus trick’. It was noted that Kirby's paper is based on the well-documented work on

\textit{PL}

classification of homotopy tori (Hsiang and Shaneson, Wall) and Sullivan's identification of the

\textit{PL}

normal invariants with

[-,G/\textit{PL}]

, but does not depend on any other work of Sullivan, documented or undocumented. This classification can be reduced to the Farrell Fibering Theorem [1], the calculation of

\pi_i(G/\textit{PL})

(Kervaire and Milnor [3]), and Wall's non-simply connected surgery theory [7].

There are modern proofs determining the homotopy type of

\textit{TOP}/\textit{PL}

using either the bounded surgery of Ferry and Pedersen [2] or a modification of the definition of the structure set.

Sullivan's determination of the homotopy type of

G/\textit{PL}

, which is well documented (for instance, in Madsen and Milgram [5]) is used to determine the homotopy type of

G/\textit{TOP}

and is fundamental to understanding the classification of general topological manifolds.

The 4-fold periodicity of the topological surgery sequence established by Siebenmann [4, p.283] contains a minor error having to do with base points. This is an easily corrected error, and the 4-fold periodicity is true whenever the manifold has a boundary.
The equivalence of the algebraic and topological surgery exact sequence as established by Ranicki [6] was confirmed. Sullivan's characteristic variety theorem, however it is understood, is not essential for the Kirby–Siebenmann triangulation of manifolds.
The following papers have been commissioned:
Singularities
Authors: Steenbrink Joseph H.M. , van Straten Duco , Vassiliev Victor A. 
Published: December 2009

The Oberwolfach workshop
Singularity Theory
was held in the week September 10th–September 15th, 2006. It was organised by J. Steenbrink (Nijmegen), D. van Straten (Mainz) and V. Vassiliev (Moskow) and continued the sequence of workshops
Singularitäten
that take place regularly at Oberwolfach.

The morning sessions consisted of three talks, which were complemented with two talks in the afternoon. So by taking the traditional Oberwolfach hike on wednesday into account, a total of

23

full hour talks was presented during the workshop.

A broad variety of topics was covered by the speakers. Normal surface singularities continue to pose some big questions which were adressed in the talks of A. Nemethi and A. Melle. The theory of motivic integration has brought the arc structure of singularities into the focus of current interest. A. Reguera and P. Popescu-Pampu reported on recent progress related to the original Nash-problem. F. Loeser reported on the first steps in non-archimedian local analytic geometry, A. Parushinski talked on conormal geometry. There has been an increased activity around global aspects of singularity theory, characteristic classes, Thom-polynomials and their applications. These topics were adressed by M. Kazarian, M. Weiss J. Schürmann and V. Sedykh. Applications of ideas from singularity theory to the geometry of the fundamental group were presented in the talks by A. Dimca, V. Kulikov and A. Libgober. S. Shadrin presented a conjectural method to produce tautological relations in the cohomology of the moduli space

\mathcal{M}_{g,n}

and O. Tommasi reported on the rational cohomology of

\mathcal{M}_{4}

. A. Gorinov talked about bounds for the size of the automorphism group of complete intersections that arise from the computation of the cohomology of the discriminant-complement. The recent interest in the Hodge/Twistor structures associated to isolated hypersurface germs and tame polynomials on affine varieties, reported on by C. Sevenheck and C. Hertling, stems partly from the interpretation of quantum cohomology via mirror symmetry in terms of so-called Landau–Ginsburg models. D. Mond talked about his idea to relate these to the theory of functions on a free divisor. J. Christophersen showed us a Calabi–Yau space appearing in the deformation theory of a degenerate abelian surface. A. Gabrielov talked about the maximally inflected rational curves and its relation to the Bethe Ansatz. A. Takahasi presented his results for exceptional collections in the category maximal Cohen–Macaulay modules on hypersurface singularities and its mirror interpretation in the case of the exceptional singularities.

An informal concert by J. Steenbrink on piano und M. Weiss on flute formed the musical coda of the workshop.
The organisers would like to use this occasion to thank the Oberwolfach staff for their efficient handling of boundary conditions, which created the unique Oberwolfach athmosphere that helped to make the workshop a success.
Geometrie
Authors: Bangert Victor , Burago Yury Dmitri , Pinkall Ulrich 
Published: December 2009

The workshop was organized by V. Bangert (Freiburg), Yu. D. Burago (St. Petersburg) and U. Pinkall (Berlin). Out of the 47 participants 22 came from Germany, 8 from the United States, 7 from Switzerland, 4 from Russia, 4 from England and 2 from France.
The official program consisted of 21 lectures and therefore left plenty of space for fruitful informal collaboration. As a tradition in this meeting there always is a series of talks that constitute a small course on a chosen topic of current interest. This time this course consisted of three lectures by V. Schroeder (Zürich) and S. Buyalo (Sankt-Petersburg) on “Asymptotic geometry of Gromov hyperbolic spaces”. In addition there were several informal talks organized by the participants, among them an evening devoted to topics related to visualization.
The program covered a wide range of new developments in geometry. These came from four major topics:
The wide range of topics provided a particularly pleasing environment for the young participants (among them six Phd-students).
Mini-Workshop: Projective Normality of Smooth Toric Varieties
Authors: Haase Christian , Hibi Takayuki , Maclagan Diane 
Published: December 2009

The mini-workshop on
Projective normality of smooth toric varieties
, organized by Christian Haase (Berlin), Takayuki Hibi (Osaka), and Diane Maclagan (New Brunswick), was held August 12th–18th, 2007. A small group of researchers with backgrounds in combinatorics, commutative algebra, and algebraic geometry worked on the conjecture that embeddings of smooth toric varieties are projectively normal. This very basic question appears in different guises in algebraic geometry, commutative algebra, and integer programming, but specific cases also arise in additive number theory, representation theory, and statistics. See the summary by Diane Maclagan for three versions of the same question.

There were a limited number of contributed talks in the mornings, setting the theme for the afternoon working groups. Monday morning began with Diane Maclagan describing the problem, and Winfried Bruns surveying the known results in the polyhedral formulation. This was followed on Tuesday morning by Benjamin J. Howard and Hidefumi Ohsugi on special cases of normality, and an
introductory talk by Milena Hering on the geometric vanishing theorem approach to the problem. On Wednesday morning Hal Schenck described a commutative algebra approach developed on site together with Greg Smith, while Sam Payne explained the Frobenius splitting approach. The commutative algebra approach, with optimization notes, continued in the talk of Ngô Viêt Trung on Thursday morning. Najmuddin Fakhruddin also explained his proof of the extended two-dimensional case on Thursday morning. Finally, on Friday we heard from Christian Haase and Andreas Paffenholz on some techniques for showing normality in special cases, and Francisco Santos on lattice Delaunay simplices which are potential starting points in search for a counterexample.
In the afternoons we split into working groups which then reported on their findings before dinner. These discussions continued through breaks, and in gaps between talks. The atmosphere of the group was very energetic, and we hope that the momentum generated during the meeting will continue with some of the ideas developed being pursued by the participants.
As a direct outcome of the workshop, we would like to mention
The organizers and participants sincerely thank the institute for providing excellent working conditions and the unique Oberwolfach spirit. We are also grateful for funding from the NSF grant supporting young US-based participants, which allowed an extra participant to attend.
In what follows we present, in addition to summaries of the talks, brief accounts on the outcome of brainstorming sessions and working groups.
Analysis and Geometric Singularities
Authors: Brüning Jochen , Mazzeo Rafe , Piazza Paolo 
Published: December 2009

The conference on “Analysis and Geometric Singularities” took place from August 19 to August 25, 2007. The meeting was a popular one, with all spots taken, and its atmosphere was lively and full of activity. Participants ranged from many experts and old hands in the field to many young postdocs and graduate students, and the interaction between researchers at all levels was clearly productive for everyone. The talks were notably very well attended throughout the week, and many were accompanied by lively discussions.
Each day was structured thematically: every day except Wednesday began with a longer (70 minute) survey talk on some general theme in the subject; the other talks each day were shorter (55 minutes) and focused on that theme. Wednesday morning, however, was devoted to five half-hour lectures by some of the younger participants. The first day's theme was spectral geometry; the lecture by Iosif Polterovich surveyed many recent results connecting spectral asymptotics and dynamics; later talks that day were given by Mueller, Kordyukov, Paycha and Grieser. Tuesday's survey talk by Mihalis Dafermos on the mathematics of black holes was followed by the lectures of Rodnianski, Vasy, Baer and Perry; the first two of these especially focusing on mathematical relativity. Thursday's survey by Jared Wunsch on propagation of singularities for the Schroedinger equation was followed by talks by Lesch, Ammann, Moscovici and Dai. Friday's theme was index theory, with a survey by Richard Melrose and other lectures by Carron, Albin, Bunke and Richardson. The young researchers who spoke on Wednesday were Azzali, Degeratu, Mazzieri, J. Mueller and Rochon.
The scientific level of the talks was uniformly high, as will be seen from the abstracts which follow; many interesting results were announced, and the survey talks helped provide a focus which in turn facilitated communication between researchers in the various different fields represented. Overall, the conference gave clear evidence that the field of analysis on singular spaces is very active, and indeed is extending in many new directions. The many strong young researchers here indicate that the field has a bright future!
Noncommutative Geometry
Authors: Connes Alain , Cuntz Joachim , Rieffel Marc A. 
Published: December 2009

Noncommutative geometry applies ideas from geometry to mathematical structures determined by noncommuting variables. Within mathematics, it is a highly interdisciplinary subject drawing ideas and methods from many areas of mathematics and physics. Natural questions involving noncommuting variables arise in abundance in many parts of mathematics and quantum mathematical physics. On the basis of ideas and methods from algebraic topology and Riemannian geometry, as well as from the theory of operator algebras and from homological algebra, an extensive machinery has been developed which permits the formulation and investigation of the geometric properties of noncommutative structures. This includes K-theory, cyclic homology and the theory of spectral triples. Areas of intense research in recent years are related to topics such as index theory, quantum groups and Hopf algebras, the Novikov- and Baum-Connes conjectures as well as to the study of specific questions in other fields such as number theory, modular forms, topological dynamical systems, renormalization theory, theoretical high-energy physics and string theory. Many results elucidate important properties of fascinating specific classes of examples that arise in many applications.
The talks covered substantial new results and insights in several of the different areas in Noncommutative Geometry. The workshop was attended by 53 participants including 6 young researchers supported by the European Union.