Mirror Symmetry and Algebraic Geometry 2015
Date:
Place:

7 – 9 Dec 2015
Conference Room (127), Graduate School of Science Bldg no.3,Department of Mathematics, Kyoto University.
Tuesday (8 Dec) afternoon talks will take place in the room 110 .

10:00–11:00

11:30–12:30

7 (Mon)Mochizuki

8 (Tue)Akaho

9 (Wed)Oouchilunch

14:00–15:00

15:15–16:15

16:30 – 17:30

WernerIwaki

Sekiguchi

Kim

HiranoMiura

Nishinou

Cho

Ikeda

Yoshikawa

Okawa

Kanazawa

18:00 –banquet

7 December
10:00 – 11:00
11:30 – 12:30
14:00 – 15:00

Takuro Mochizuki
Elisabeth Werner
Kohei Iwaki

A Twistor Approach to Kontsevich Complexes
Orbifold Jacobian Algebras for Invertible Polynomials
Topological recursion, quantum curves and Painlevé

15:15 – 16:15

Jiro Sekiguchi

equations
A generalization of WDVV equation and its applications

16:30 – 17:30

Bumsig Kim

Mirror Theorem for Elliptic Quasimap Invariants

10:00 – 11:00

Manabu Akaho

11:30 – 12:30

Yuki Hirano

Symplectic displacement energy for exact Lagrangian
immersions
Equivalences of derived factorization categories of gauged

14:00 – 15:00

Makoto Miura

Landau-Ginzburg models
Complete intersection Calabi–Yau threefolds in Grassmannians

15:15 – 16:15
16:30 – 17:30

Takeo Nishinou
Cheol-Hyun Cho

with respect to homogeneous vector bundles
Degeneration and curves on K3 surfaces
Constructive mirror functor for punctured Riemann surfaces

8 December

9 December
10:00 – 11:00
11:30 – 12:30

Genki Oouchi
Akishi Ikeda

Lagrangian embeddings of cubic fourfolds containing a plane
Stability conditions on Calabi-Yau completions for formal
parameters

14:00 – 15:00
15:15 – 16:15

Ken-Ichi Yoshikawa
Shinnosuke Okawa

BCOV invariant for Borcea-Voisin threefold
Compact moduli of marked noncommutative cubic surfaces

Atsushi Kanazawa

via quivers
A partial compactification of the Hori-Vafa toric mirror
symmetry

16:30 – 17:30

This workshop is supported by Grant-in-Aid for Challenging Exploratory Research 26610008(Takahashi).
Organizers: Hiroshi Iritani, Yukiko Konishi, Atsushi Takahashi

1Abstracts• Manabu Akaho
Title: Symplectic displacement energy for exact Lagrangian immersions
Abstract: In this talk, I will explain an inequality of displacement energy for exact Lagrangian immersions. Our approach is based on Floer homology for Lagrangian immersions
and Chekanov’s homotopy technique of continuations.
• Cheol-Hyun Cho
Title: Constructive mirror functor for punctured Riemann surfaces
Abstract: We propose a non-commutative mirror symmetry formalism. Given a family ofLagrangian submanifold in a symplectic manifold, we use Maurer-Cartan formalism to define
the mirror non-commutative quiver algebra, with a central element, such that it comes witha canonical A-infinity functor from Fukaya category of the symplectic manifold to the matrix
factorization category of this central element. We illustrate this in the case of punctured
Riemann surfaces, recovering Bocklandt’s result in a geometric way. This is a joint workwith Hansol Hong and Siu-Cheong Lau.
• Yuki Hirano
Title: Equivalences of derived factorization categories of gauged Landau-Ginzburg models
Abstract: Derived factorization categories of gauged Landau-Ginzburg (LG) models are generalizations of bounded derived categories of coherent sheaves on varieties, and are considered as the categories of D-brane of type B for gauged LG models. In this talk, for a given
Fourier-Mukai equivalence of bounded derived categories of coherent sheaves on smooth quasiprojective varieties, we obtain Fourier-Mukai equivalences of derived factorization categoriesof gauged LG models. As an application, we show some equivalences of derived factorization
categories of K-equivalent gauged LG model.
• Akishi Ikeda
Title: Stability conditions on Calabi-Yau completions for formal parameters
Abstract: The aim of this talk is to define the space of stability conditions on an s-Calabi-Yau
category for a complex number s. For this purpose, we introduce a Calabi-Yau completion
for a formal parameter and a variation of a Bridgeland stability condition on it. We also
discuss the relationship between central charges of these stability conditions on Calabi-Yau
completions of ADE-quivers and twisted periods of ADE-singularities.
• Kohei Iwaki
Title: Topological recursion, quantum curves and Painlevé equations
Abstract: In this talk, I ll explain about a relationship between the Eynard-Orantin s
topological recursion and Painlevé equations. More precisely, generalizing some results ofEynard-Orantin and their collaborators, we ll show that the free energy defined by the
topological recursion gives a tau-function the Painlevé equations (for the first and the secondequations; work in progress for other Painlevé equations). Moreover, we ll see that the
topological recursion also recover the isomonodromy linear system (as a quantum curve) for
these Painlevé equations form their spectral curve. This talk is based on the joint work with
Olivier Marchal (Lyon) and Axel Saenz (UC Davis).
2• Atsushi Kanazawa
Title: A partial compactification of the Hori-Vafa toric mirror symmetryAbstract: In this talk, I will introduce a partial compactification of mirror symmetry fora class of toric Calabi-Yau manifolds, discussing a new connection between SYZ mirror
symmetry and modular forms. This also gives an insight into mirror symmetry for varietiesof general type (for example, Seidel’s work on genus two Riemann surfaces). If time permits,
I will discuss a higher dimensional analogue of the Yau-Zaslow formula for an elliptic K3
surface. This talk is based on a joint work with Siu-Cheong Lau.
• Bumsig KimTitle: Mirror Theorem for Elliptic Quasimap Invariants
Abstract: This is a joint work with Hyenho Lho. We present a mirror theorem for the elliptic
quasimap invariants of smooth Calabi-Yau complete intersections in projective spaces. The
theorem combined with the wall-crossing formula implies mirror theorems of Zinger andPopa for the elliptic Gromov-Witten invariants of those varieties. The theorem and the wallcrossing formula provide a unified framework for the mirror theory of rational and elliptic
Gromov-Witten invariants.
• Makoto Miura
Title: Complete intersection Calabi–Yau threefolds in Grassmannians with respect to homogeneous vector bundles
Abstract: I will talk about recent joint works with Daisuke Inoue and Atsushi Ito, on complete
intersection Calabi–Yau threefolds in Grassmannians with respect to homogeneous vector
bundles. We focus on those Calabi–Yau threefolds with Picard number one and describe
their geometry. I will also explain the computation of the I-functions of those Calabi– Yauthreefolds and discuss the mirror construction via conifold transition.
• Takuro Mochizuki
Title: A twistor approach to Kontsevich complexes
Abstract: Kontsevich complexes are families of complexes associated to algebraic functions
on smooth complex algebraic varieties. The concept was introduced by M. Kontsevich in hisstudy on the B-side of mirror symmetry. In this talk, we revisit some interesting results dueto H. Esnault, M. Kontsevich, C. Sabbah, M. Saito and J.-D. Yu on Kontsevich complexes
from a twistor viewpoint. After a brief review on the general theory of mixed twistor Dmodules, we explain how to apply it to obtain the results on Kontsevich complexes. We hopethat this viewpoint would be useful to understand the generalized Hodge theoretic propertyof Kontsevich complexes.
• Takeo Nishinou
Title: Degeneration and curves on K3 surfaces
Abstract: A folklore conjecture concerning rational curves on K3 surfaces states that allK3 surfaces contain infinite number of irreducible rational curves. It is known that all K3
surfaces, except those contained in the countable union of hypersurfaces in the moduli spaceof K3 surfaces satisfy this property. In this talk, we present a new approach to this problem

3and prove that there is a Zariski open dense subset in the moduli space of quartic K3 surfaces
whose members satisfy the conjecture. We also mention the case of more general K3 surfaces.
• Shinnosuke Okawa
Title： Compact moduli of marked noncommutative cubic surfaces via quivers
Abstract: I will explain in some detail about the compactified moduli spaces of marked
noncommutative cubic surfaces constructed by using quivers. In particular I will show how
the moduli spaces of quiver representations are used to recover the data of a noncommutative
projective plane plus six points on it from the given relations of the quiver. This is a joint
work with Tarig Abdelgadir and Kazushi Ueda.
• Genki Oouchi
Title： Lagrangian embeddings of cubic fourfolds containing a plane
Abstract: For a cubic 4-fold X not containing a plane, Lehn et al constructed an irreducible
holomorphic symplectic 8-fold which contains X as a Lagrangian submanifold via twisted
cubic curves on X. In this talk, I will talk about Lagrangian embeddings of cubic 4-folds
containing a plane. The desired irreducible holomorphic symplectic 8-fold can be constructed
as a moduli space of Bridgeland stable objects on the derived categories of twisted K3 surfaces.
• Jiro Sekiguchi
Title: A generalization of WDVV equation and its applications
Abstract: The WDVV equation arose from 2D topoligical field theory. In this talk, I introduce a generalization of WDVV equation and apply it to flat coordinate system for irreducible
well-generated complex reflection groups and Painlevé VI. This is a joint work with M. Katoand T. Mano.
• Elizabeth Werner
Title: Orbifold Jacobian Algebras for Invertible Polynomials
Abstract: Let f be a quasihomogeneous polynomial with an isolated singularity at the origin.
The Jacobian algebra of f is the local algebra of its partial derivatives. It is finite dimensionaland has the structure of a Frobenius algebra. We consider a group action on f. Let G be a
finite group of symmetries of f. The pair (f,G) is often called a Landau-Ginzburg orbifold.
We want to construct an orbifold version of the Jacobian algebra for the pair (f,G). This isa joint work with Alexey Basalaev and Atsushi Takahashi.
• Ken-Ichi Yoshikawa
Title: BCOV invariant for Borcea-Voisin threefold
Abstract: BCOV invariant is a holomorphic torsion invariant of Calabi-Yau threefold, giving
the genus-one string amplitude in B-model. Mirror symmetry at genus-one is formulated
as an explicit infinite product expression of the BCVO invariant near the large complex
structure limit point in terms of genus-one instant numbers. In this talk, I will explain anexplicit formula for the BCOV invariant for Borcea-Voisin threefolds. If time permits, I will
also explain the construction of BCOV invariant for Calabi-Yau orbifolds and its twisted
version, as well as some of their properties.

4