## The Frobenius conjecture in dimension two

the mirror of log Calabi-Yau surfaces. In particular, we prove the Frobenius structure conjecture

of Gross-Hacking-Keel in dimension two. *This is joint work with Sean Keel.

Tony Yue Yu

IAS

March 16, 2017

Abstract: We apply the counting of non-Archimedean holomorphic discs to the construction of

the mirror of log Calabi-Yau surfaces. In particular, we prove the Frobenius structure conjecture

of Gross-Hacking-Keel in dimension two. *This is joint work with Sean Keel.

the mirror of log Calabi-Yau surfaces. In particular, we prove the Frobenius structure conjecture

of Gross-Hacking-Keel in dimension two. *This is joint work with Sean Keel.

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

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

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

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

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.

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.

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

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

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.

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.

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.

Ludmil Katzarkov

IAS

March 17, 2017

Abstract: In this talk we will combine classical mathematical structures and we will look at them

from a new prospective. Applications to geometry will be considered.

from a new prospective. Applications to geometry will be considered.

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.

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?