Video Lectures

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...

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...

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...

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...

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...

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...

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...

Abstract: In this talk we will report on joint work in progress with Mohammed Abouzaid concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the derived category of the hypersurface and the Fukaya category of the...

Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems defined on Riemann surfaces. These are categorical...