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
IAS
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.

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

On small sums of roots of unity

Philipp Habegger
University of Basel
March 9, 2017

Let $k$ be a fixed positive integer. Myerson (and others) asked how small the modulus of a non-zero sum of $k$ roots of unity can be. If the roots of unity have order dividing $N$, then an elementary argument shows that the modulus decreases at most exponentially in $N$ (for fixed $k$). Moreover it is known that the decay is at worst polynomial if $k < 5$. But no general sub-exponential bound is known if $k \geq 5$.

On the role of rank in representation theory of the classical groups

Roger Howe
Yale University and Texas A & M University
March 8, 2017
Rank gives a natural filtration on representations of classical groups. The eta correspondence provides a clean description of a natural family of representations of a given rank, subject to certain bounds. There is evidence that this construction produces all representations of small rank.