Date: 2017 September 25 (Mon) - 26 (Tue)
Venue: Kyoto University, Department of Mathematics (Science Building 3), Room 110.
Mark Gross (Cambridge University)
His lecture was cancelled this time and will be given some time in the next year.
Martin Guest (Waseda University)
::: A general theory of tt*-Toda equations :::
Cecotti-Vafa introduced the tt* equations as a tool for classifying massive deformations of quantum field theories (and certain Fano varieties). Dubrovin gave a mathematical formulation of the tt* equations as isomonodromy equations, demonstrating their integrability. Cecotti-Vafa pointed out several examples of tt* equations of "Toda type", which are expected to be integrable in a stronger sense. We shall sketch a general theory of these tt*-Toda equations associated to a complex simple Lie group G.
Shinobu Hosono (Gakushuin University)
::: Movable vs monodromy nilpotent cones of Calabi-Yau manifolds :::
Birational geometry of Calabi-Yau manifolds in mirror symmetry is a classical subject studied since 90's. In old days, this subject was studied mostly for Calabi-Yau hypersurfaces in toric varieties. I will focus on Calabi-Yau complete intersections described by Gorenstein cones, for which we find interesting birational geometries and also the corresponding degenerations in the moduli space of mirror Calabi-Yau manifolds. For each degeneration, we have the so-called monodromy nilpotent cone. I will show two specific examples for which the monodromy nilpotent cones are glued together to make a larger cone which we identify with the movable cone slightly modified by first order quantum corrections. This talk is based on a recent paper with H. Takagi (arXiv:1707.08728).
Kohei Iwaki (Nagoya University)
::: Stokes structure of equivariant CP1 and wall-crossing :::
I'll investigate the quantum differential equation for the equivariant CP1 model (= the Gauss-Manin system for the mirror oscillatory integral) via the exact WKB method. In particular, I introduce and compute the total Stokes matrix for this equation, and examine the 2d-4d wall-crossing formula proposed by Giotto-Moore-Neitzke. I'll also mention about a (re)construction of the quantum differential equation through the topological recursion. My talk is based on the joint work with H. Fuji (Kagawa), M. Manabe (Warsaw) and I. Satake (Kagawa).
Hyenho Lho (ETH Zurich)
::: Stable quotients and holomorphic anomaly equation :::
In first lecture, I will review Givental-Teleman's classification theorem for semi-simple cohomological field theory and give a proof of this theorem in case of Gromov-Witten invariant or stable quotient invariants of varieties with good torus action. In the second lecture I will prove the holomorphic anomaly equation for the stable quotient invariant of local CP2 in the precise form predicted by B-model physics. If I have more time, I will also prove the holomorphic anomaly equation for [C3/Z3] and formal quintic invariants. This talk is based on joint work with Rahul Pandharipande.
Yoshinori Namikawa (Kyoto University)
::: Towards the classification of symplectic singularities :::
After introducing the finiteness theorem for symplectic singularities, I will give a characterisation of nilpotent orbit closures of a complex semisimple Lie algebra and their finite coverings.
Kaoru Ono (Kyoto RIMS)
::: Twisted sectors in Lagrangian Floer theory :::
I will speak on a notion of twisted sectors in Lagrangian Floer theory in an appropriate setting. I also discuss it in some typical example and necessary ingredients to construct a theory. It is based on a joint work (in progress) with Bohui Chen and Bai-Ling Wang.
Atsushi Takahashi (Osaka University)
::: On orbifold Jacobian algebras for invertible polynomials :::
Motivated by some algebraic structures on the pair of Hochshild cohomology and homology groups, we propose an axiom for the "orbifold Jacobian algebra", the Jacobian algebra for a pair of isolated hypersurface singularity and a finite group preserving the defining polynomial of the singularity, in physics terminology, the B-model chiral algebra for Landau-Ginzburg orbifolds. We show the existence and the uniqueness of the orbifold Jacobian algebra for an invertible polynomial and its symmetry group. The relation to the category of equivariant matrix factorizations will also be given. This is a joint work with Alexey Basalaev and Elisabeth Werner.