Real Lagrangians in toric degenerations

Bernd Siebert
University of Hamburg
March 17, 2017
Abstract: Real loci of the canonical toric degenerations constructed from integral affine
manifolds with singularities in the joint work with Mark Gross, provide an ample source of
examples of Lagrangians that conjecturally are amenable to algebraic-geometric versions of
Floer theory. In the talk I will discuss joint work with Hülya Argüz on how the topology of the real
locus can be understood by means of the affine geometry and by Kato-Nakayama spaces
associated to log spaces.

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

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

Calabi-Yau geometry and quantum B-model

Si Li
Tsinghua University
March 17, 2017
We discuss the Kadaira-Spencer gauge theory (or BCOV theory) on Calabi-Yau geometry. We explain Givental's loop space formalism at cochain level which leads to a degenerate BV theory on Calabi-Yau manifolds. Homotopic BV quantization together with a splitting of the Hodge filtration lead to higher genus B-model. We illustrate such quantization and higher genus mirror symmetry by the elliptic curve example.

"Small" representations of finite classical groups

Shamgar Gurevich
University of Wisconsin and Yale University
March 8, 2017

Suppose you have a finite group G and you want to study certain related structures (e.g., random walks, Cayley graphs, word maps, etc.). In many cases, this might be done using sums over the characters of G. A serious obstacle in applying these Fourier type formulas is lack of knowledge on the low dimensional representations of G. In fact, numerics shows that the "small" representations tend to contribute the largest terms to these sums, so a systematic knowledge on them might assist in the solution of important problems.