Workshop on Homological Mirror Symmetry and Related Topics
January 21-26, 2008, University of Miami

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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.