Sergei Gukov (UC Santa Barbara): Gauge Theory and Categorification
Maxim Kontsevich (IHES and U. Miami): Motivic Donaldson-Thomas invariants
These lectures are about my recent work with Y. Soibelman. We propose a general algebraic framework for the counting of objects in 3-dimensional CY categories, and a wall-crossing formula describing the dependence of invariants under the change of the stability condition.David Nadler (Northwestern): Loop Spaces in Representation Theory
Dmitri Orlov (RAS): Derived categories of coherent sheaves, triangulated categories of singularities and D-branes in LG-models
Mohammed Abouzaid (Clay Institute and MIT): TBA
Marco Aldi (Berkeley): A-branes and (non-commutative) coordinate rings
Marco Gualtieri (MIT): Generalized complex 4-manifolds
By investigating 2-branes in generalized complex 4-manifolds, I will explain how Cavalcanti and I produced interesting examples of generalized complex 4-manifolds, including the triple connect sum of CP2 with itself.Daniel Huybrechts (Univ. Bonn): Deformations of Fourier-Mukai equivalences and applications
Under certain cohomological conditions a derived equivalence between K3 surfaces can be deformed sideways. I shall explain how to use this technique to deduce results about derived equivalences, stability conditions and Chow groups for projective K3 surfaces from the geometrically easier situation of a generic non-projective K3 surface. (Partially joint work with Macri and Stellari.)Joel Kamnitzer (AIM, Berkeley): Knot homology via derived categories of coherent sheaves
Alexander Kuznetsov (RAS): Derived categories of Fano 3-folds
Derived categories of Fano 3-folds have semiorthogonal decompositions usually consisting of two exceptional vector bundles and an additional component. I will explain how some of this nontrivial component can be described. In particular, I will discuss a strange relation between derived categories of Fano 3-folds of index 1 and even genus and derived categories of Fano 3-folds of index 2.Davesh Maulik (Clay Institute and Columbia): TBA
Grigory Mikhalkin (U. Toronto): Phase-tropical curves
Kaoru Ono (Hokkaido Univ.): Tensor product of filtered A_infty-algebras
Tony Pantev (U. Penn.): Generalized Hodge structures and mirror symmetry
Jake Solomon (Princeton): Differential equations for open Gromov-Witten invariants
Chris Woodward (Rutgers): Functoriality for Gromov-Witten invariants under symplectic quotients
I will give an overview of a project of a number of people, including K. Wehrheim, S. Ma'u, F. Ziltener, E. Gonzalez, and myself. The project is to (i) define a notion of morphism of CohFT's, which complexifies the notion of A-infinity morphism, (ii) show (building on Ziltener's thesis) that there is a canonical "quantum Kirwan" morphism of CohFT's from the equivariant GW theory of a Hamiltonian G-manifold to the GW theory of its quotient, and (iii) prove a "quantum non-abelian localization" formula relating the correlators.