Video Lectures

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.

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...

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...

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...

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...