Christopher Beem
- TITLE: The (super)conformal bootstrap
- ABSTRACT: My first lecture will be an overview of the bootstrap approach to strongly coupled conformal field theories and the motivations for pursuing such an approach. My second lecture will address special features of the bootstrap problem that arise in the context of theories with large amounts of supersymmetry.

Philip Candelas
- TITLE: Counting $F_p$—rational points, zeta functions and speculations on the action of mirror symmetry
- ABSTRACT: This talk will describe little that is new, though there has been technical progress in counting $F_p$—rational points, for one—parameter families of Calabi—Yau manifolds. We are led to compute the zeta—functions for these families and these computations suggest a role for mirror symmetry.

Sergei Gukov
- TITLE: Numbers in complex Chern-Simons theory

Jeff Harvey
- TITLE: Lifting symmetries in CFT and Conway subgroup compactifications of heterotic string
- ABSTRACT: I will discuss the general issue of lifting lattice symmetries in Conformal Field Theory. For example, T-duality which exchanges small and large radius in string theory, is order two acting on the moduli space of string compactifications but order four in its action on the CFT. I will discuss an application of this formalism to asymmetric orbifolds and then use this to construct some compactifications of the heterotic string with subgroups of the Conway group acting as symmetries of the BPS spectrum. The talk is based on joint work with Greg Moore.

Yang-Hui He
- TITLE: Calabi-Yau, Quivers, & Dessins d'Enfants
- ABSTRACT: We discuss how bipartite graphs on Riemann surfaces encapture a wealth of information about the physics and the mathematics of gauge theories. The correspondence between the gauge theory, the underlying algebraic geometry of its space of vacua as a quiver variety, the combinatorics of dimers and toric varieties, as well as the number theory of dessin d'enfants becomes particularly intricate under this light.

Minhyoung Kim
- Title: Arithmetic geometry for physicists
- Abstract: This series will present a brief introductory survey of Galois representations, automorphic forms, L-functions, and Diophantine geometry, together with speculation on how physics might be useful in studying these objects

Albrecht Klemm
- TITLE: D-brane masses and the motivic Hodge conjecture
- ABSTARCT: We consider the one parameter mirror family W of the quintic in P^4. By mirror symmetry the even Dp-brane masses of the quintic M can be identified with four periods w.r.t to an integral symplectic basis of H_3(W,Z) at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the L-function of the weight four holomorphic Hecke eigenform with eigenvalue one of Gamma_0(25), that was found by Chad Schoen in this context and whose coefficients a_p count the number of solutions of the mirror quinitic at the conifold over the finite number field F_p as was discovered by del la Ossa, Candelas and Villegas. Using the theory of periods and quasi-periods of Gamma_0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point.

Wei Li
- TITLE: W symmetry, affine Yangian, and plane partitions
- ABSTRACT: I will talk about a triangle connecting the three objects in the title. I will explain (1) How affine Yangian and W symmetry are related. (2) Plane partitions furnish a natural class of representations for affine Yangians. (3) Plane partition provides a useful new way to study representation of W algebra. (Time permitted, I will illustrate the last point with one or two examples motivated by higher spin gravity and string theory.)

Sameer Murthy
- TITLE: Squashed toric sigma models and mock modular forms
- ABSTRACT: In the late 80s and early 90s a three-way link was established between N=(2,2) SCFTs, compact Calabi Yau (CY) manifolds, and modular/Jacobi forms. These links can be understood through the corresponding Gauged Linear Sigma Models and calculations of their elliptic genera. I will discuss how there are interesting modifications to these links when the spectrum involves a continuum. The corresponding players in the new relations are non-compact N=(2,2) SCFTs, squashed toric manifolds, and mock modular/mock Jacobi forms and generalizations.

Pavel Putrov
- TITLE: Integrality in analytically continued Chern-Simons theory
- ABSTRACT: Physics predicts existence of homological invariants of closed oriented 3-manifolds similar to Khovanov-Rozansky homology of knots in a 3-sphere. The decategorified version of such invariants are q-series with integer coefficients. In my talk I will discuss properties of such invariants, how they are related to Chern-Simons partition function (WRT invariant) analytically continued w.r.t. level, and give some examples. For a certain class of 3-manifolds the corresponding q-series have mock-modular properties. If time permits I will also discuss how resurgence theory can be used to construct such invariants.

Fernando Rodriguez-Villegas
- TITLE: Mixed Hodge structure of character varieties
- ABSTRACT: In this talk I will discuss the conjectures with Hausel and Letellier that describe the mixed Hodge structure of the character varieties parameterizing finite dimensional representations of the fundamental group of a Riemann surface. The formulation of these conjectures involve the Macdonald polynomials and arose from counting points of the varieties over finite fields.

Philsang Yoo
- TITLE: Classical Field Theories for Quantum Geometric Langlands
- ABSTRACT: One can study a class of classical field theories in a purely algebro-geometric framework, thanks to the recent development of derived symplectic geometry. After discussing the basics of derived symplectic geometry, I will explain some interesting examples of classical field theories in this framework, including B-model, Chern-Simons theory, and Kapustin-Witten theory. In the last part of the talk, I will make a proposal to understand quantum geometric Langlands and other related Langlands dualities in a unified way from the perspective of field theory.

Noriko Yui
- TITLE: Supercongruences for rigid hypergeometric Calabi–Yau threefolds
- ABSTRACT: We will present two proofs to the supercongruences for the fourteen rigid hypergeometric Calabi–Yau threefolds defined over the rationals. The existence of such supercongruences was conjectured (based on numerical evidence) by F. Rodriguez-Villegas in 2003. This is a joint work with Ling Long, Fang-Ting Tu and Wadim Zudilin.

Don Zagier
- TITLE: Quantum Invariants, Modular Forms, and Algebraic K-theory