DONAGI, Ron　(University of Pennsylvania)

Hitchin systems, mirror symmetry, and geometric Langlands duality

FUKAYA, Kenji　(Kyoto University)

Floer theory of orbits in toric manifolds

In this talk I will explain the calculation of filtered A infinity algebra of the orbits of (arbitrary compact) toric manifold. The calculation is based on earlier works by Cho and Oh. As an application we show that there exists at least one orbit T which has nontrivial Floer homology and hence undisplacable. Namely there is no Hamiltonian diffeomorphism F such that F(T) is disjoint from T. There are related earlier works by Cho-Oh, Entov-Polterovich, Cho. We use the mechinary of obstruction and deformation theory of Lagrangian Floer homology ([FOOO]) in its full genearlity for the proof. Relations to the mirror symmetry between toric manifold and LG model is mentioned.

GROSS, Mark　(University of California, San Diego)

The tropical vertex

I will describe work in progress, joint with Bernd Siebert, which relates enumerative calculations of curves in weighted projective planes to certain factorizations of commutators in a group of symplectomorphisms introduced by Kontsevich and Soibelman. This can be viewed as a key part of understanding mirror symmetry, playing the role of an "inductive step" for comparing the calculation of Gromov-Witten invariants on the A-model side of mirror symmetry for Calabi-Yau manifolds and the B-model side (period calculations).

HERTLING, Claus　(University Mannheim)

Hypersurface singularities and tt^* geometry

tt^* geometry means the variation of a datum which generalizes a polarized Hodge structure and which consists of a vector bundle on P^1 with a meromorphic connection with poles of order two at 0 and infinity, with a real structure and a pairing with some conditions. It was first considered by Cecotti and Vafa; it is related to Simpson's harmonic bundles and recent work of Sabbah and Mochizuki. One source of such a structure are oscillating integrals of hypersurface singularities. I will discuss nilpotent orbits, classifying spaces and period maps, in general and in the case of hypersurface singularities. Part of it is joint work with Christian Sevenheck.

IRITANI, Hiroshi　(Kyushu University)

Wall-crossing in toric Gromov-Witten theory

KIM, Bumsig　(KIAS)

A compactification of the space of maps from curves

We will present a new compactification of the moduli space of maps from pointed nonsingular complex projective stable curves to a nonsingular complex projective variety with prescribed ramification indices at the points. It will be explained that the compactification is a proper DM-stack equipped with a natural virtual fundamental class. This is joint work with A. Kresch and Y.-G. Oh.

LEUNG, Naichung Conan　(Chinese University of Hong Kong)

On the SYZ mirror transformation

In this talk, we will discuss the Strominger-Yau-Zaslow mirror transformation, which is a Fourier-Mukai transformation along Lagrangian fibrations. We will apply this to explain quantum corrections in the Fano toric manifolds cases.

LI, Jun　(Stanford University)

Towards high genus GW-invariants of quintic Calabi-Yau threefold

MOCHIZUKI, Takuro　(Kyoto University)

On wild harmonic bundles

We will give an overview of our recent study on wild harmonic bundles. We hope to mention the application to wild pure twistor D-modules.

MULASE, Motohico　(University of California, Davis)

Matrix integral approach to character varieties

Matrix integral techniques are useful for the study of intersection theory of cohomology classes on the moduli space of Riemann surfaces. So far such an approach has not been developed for the moduli spaces of vector bundles on Riemann surfaces. In this talk a new approach using a generalized matrix integral is presented. This is a joint work with Jerry Kaminker.

PANDHARIPANDE, Rahul　(Princeton University)

Open descendent integrals

PANTEV, Tony　(University of Pennsylvania)

Generalized Hodge structures and mirror symmetry

I will discuss the Hodge theory of non-commutative spaces of Calabi-Yau type and its interaction with mirror symmetry. This is a joint work in progress with L.Katzarkov and M.Kontsevich.

NEKRASOV, Nikita　(Institut des Hautes Études Scientifiques (IHES))

Lessons from low dimensional topological strings

SABBAH, Claude　(E'cole Polytechnique)

Quantum cohomology of the Grassmannian and alternate Thom-Sebastiani

I will report on a joint work with Bumsig Kim, where we introduce the notion of alternate product of Frobenius manifolds and we give an interpretation of the Frobenius manifold structure canonically attached to the quantum cohomology of the Grassmannian in terms of alternate products. On the mirror side, we also investigate the relationship with the alternate Thom-Sebastiani product of Laurent polynomials.

SAITO, Masa-Hiko,　(Kobe University)

Moduli spaces of linear connections and Riemann-Hilbert correspondences

We will discuss about the construction of moduli spaces of linear connections over a curve with prescribed types of regular or irregular singularities by Mumford's GIT. Moreover constructing also the moduli spaces of Monodromy-Stokes data, we can define and study Riemann-Hilbert correspondences in details. Iso-monodromy-Sokes deformations of the connections defines natural flows on the family of the moduli spaces of linear connectios. We will investigate the relationship between the flows and various integrable systems.

STIENSTRA, Jan　(Utrecht University)

Two-variable hypergeometric systems and dessins d'enfants

A recently discovered relation between on the one hand two-variable hypergeometric systems and on the other hand dessin d'enfants (graphs embedded in surfaces) will be discussed. This includes: (1) the role of the secondary polytope. (2) the observation that the characteristic cycle (or principal A-determinant) of the Hypergeometric D-module equals the determinant of the bi-adjacency matrix which describes the dessin d'enfants. (3) the size of the bi-adjacency matrix equals the dimension of the solution space of the GKZ hypergeometric system of differential equations. (4) perfect matchings on dimer models are refinements of the triangulations of the primary polytope in GKZ theory.

TAKAHASHI, Atsushi　(Osaka University)

Mirror Symmetry of Isolated Hypersurface Singularities

Existence of a strongly exceptional collection for the triangulated category of a graded isolated hypersurface singularity in one dimension will be shown. In particular, this triangulated category turns out to be equivalent to the derived category of finite dimensional representations of a finite dimensional algebra given by quivers and relations, which corresponds to the Seifert matrix for a distinguished basis of vanishing cycles in the Milnor fiber of the "mirror" singularity.

TAKASAKI, Kanehisa　(Kyoto University)

Integrable structure in melting crystal model of 5D gauge theory

I will report a recent result on integrable structures in a 5D analogue of Nekrasov's instanton partition function for supersymmetric gauge theories. This partition function is formulated as a statistical model of random plane partition known as ``melting crystal''. By adding new potential terms and viewing the coupling constants as fictitious ``time variables'', the partition function turns out to be a tau function of the 1-Toda hierarchy. A fermionic realization of quantum torus Lie algebra plays a central role in identifying this integrable structure. This is a joint work with Toshio Nakatsu.

TODA, Yukinobu　(University of Tokyo)

Limit stable objects on Calabi-Yau 3-folds