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.

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

Equivariant geometry and Calabi-Yau manifolds

Daniel Halpern-Leistner
Columbia University
March 16, 2017
Abstract: Mirror symmetry has led to deep conjectures regarding the geometry of Calabi-Yau
manifolds. One of the most intriguing of these conjectures states that various geometric
invariants, some classical and some more homological in nature, agree for any two Calabi-Yau
manifolds which are birationally equivalent to one another. I will discuss how new methods in
equivariant geometry have shed light on this conjecture over the past few years, ultimately

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

Descent and equivalences in non-commutative geometry

Tony Pantev
University of Pennsylvania
March 16, 2017
Abstract: I will describe descent formalism in categorical non-commutative geometry which is
geared towards constructions of Fourier–Mukai functors. The formalism allows one to carry out
descent constructions in general algebraic and analytic frameworks without resorting to
generators. I will discuss various applications, such as the connection to the classical Zariski and
flat descents, constructions of Fukaya categories, and homological mirror symmetry. This is a
joint work with Katzarkov and Kontsevich.

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

Central charges of B-branes at non geometric phases

Mauricio Romo
IAS
March 16, 2017
Abstract: I'll give an overview of basic concepts about B-branes and their central charges and
how they arise in physics and mathematics. In particular I'll present the gauge linear model
approach which allows for defining quantities in the full stringy Kahler moduli M of certain
Calabi-Yaus (CY). Then, I'll show some examples and motivate an intrinsic definition of the central
charges on phases (some sub-regions of M), based on field theory data. I'll put particular