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

Moduli spaces of elliptic curves in toric varieties

Dhruv Ranganathan
IAS
March 16, 2017
Abstract: The moduli spaces of stable maps to toric varieties occur naturally in enumerative
geometry and mirror symmetry. While they have several pleasing properties, they are often
quite singular, reducible, and non-equidimensional. When the source curves have genus 0, the
situation is markedly improved by adding logarithmic structure to the moduli problem. This
produces irreducible and non-singular moduli spaces of rational curves in toric varieties, whose

Efficient non-convex polynomial optimization and the sum-of-squares hierarchy

David Steurer
Cornell University; Member, School of Mathematics
March 20, 2017

The sum-of-squares (SOS) hierarchy (due to Shor'85, Parrilo'00, and Lasserre'00) is a widely-studied meta-algorithm for (non-convex) polynomial optimization that has its roots in Hilbert's 17th problem about non-negative polynomials.

SOS plays an increasingly important role in theoretical computer science because it affords a new and unifying perspective on the field's most basic question:

What's the best possible polynomial-time algorithm for a given computational problem?

Approximate counting and the Lovasz local lemma

Ankur Moitra
Massachusetts Institute of Technology
March 20, 2017

We introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Moreover our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random.

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
Cornell
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