Brane structures from the perspective of microlocal sheaf theory

Xin Jin
Northwestern Univ
March 13, 2017
Abstract: In this talk, I will present the following application of microlocal sheaf theory in
symplectic topology. For every closed exact Lagrangian L in the cotangent bundle of a manifold
M, we associate a locally constant sheaf of categories on L, which we call Brane_L, whose fiber is
the infinity-category of k-modules, for k any ring spectrum. I will discuss the relation of Brane_L
with the usual brane structures in Floer theory, and its connection to the J-homomorphism in

Topological Fukaya categories with coefficients

Tobias Dyckerhoff
University of Bonn
March 13, 2017
Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical
coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems
defined on Riemann surfaces. These are categorical analogues of perverse sheaves, called
perverse schobers. We provide a definition of perverse schobers as categorical sheaves on a
relative two-colored version of the unital Ran space of the surface. We explain how to describe

Towards homological mirror symmetry for complete intersections in toric varieties

Denis Auroux
March 13, 2017
Abstract: In this talk we will report on joint work in progress with Mohammed Abouzaid
concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the
derived category of the hypersurface and the Fukaya category of the mirror Landau-Ginzburg
model. We will then discuss the extension of these results to (essentially arbitrary) complete
intersections in toric Fano varieties.

Mirror symmetry for minuscule flag varieties

Nicolas Templier
March 15, 2017
Abstract: We prove cases of Rietsch mirror conjecture that the A-model of projective
homogeneous varieties is isomorphic to the B-model of its mirror, which is a partially
compactified Landau--Ginzburg model constructed from Lie theory and geometric crystals. The
conjecture relates to deep objects in algebraic combinatorics. Our method of proof comes from
Langlands reciprocity, and consists in identifying the quantum connection as Galois and the
crystal as automorphic. I will mention further potential interactions between symplectic

Mirror symmetry for homogeneous varieties

Clelia Pech
Kent University
March 15, 2017
Abstract: In this talk reporting on joint work with K. Rietsch and L. Williams, I will explain a new
version of the construction by Rietsch of a mirror for some varieties with a homogeneous Lie
group action. The varieties we study include quadrics and Lagrangian Grassmannians (i.e.,
Grassmannians of Lagrangian vector subspaces of a symplectic vector space). The mirror takes
the shape of a rational function, the superpotential, defined on a Langlands dual homogeneous

Vertex algebras, quantum master equation and mirror symmetry

Si Li
Tsinghua University
March 15, 2017
Abstract: We study the effective BV quantization theory for chiral deformation of two
dimensional conformal field theories. We establish an exact correspondence between
renormalized quantum master equations for effective functionals and Maurer-Cartan equations
for chiral vertex operators. The generating functions are proven to be almost holomorphic
modular forms. As an application, we construct an exact solution of quantum B-model (BCOV
theory) in complex one dimension that solves the higher genus mirror symmetry conjecture on