Homological Mirror Symmetry

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: 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: 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: I plan to discuss the definition of open descendent integrals. In genus g>0, this involves the moduli space of Riemann surfaces with boundary with an additional structure called a grading. *Joint work with R. Tessler.

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...

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, I will present the following application of microlocal sheaf theory in symplectic topology. For every closed exact Lagrangian L in the cotangent bundle of a manifold M, we associate a locally constant sheaf of categories on...

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...

Please see agenda: http://www.ias.edu/math/files/Workshop%20on%20Homological%20Mirror%20SymmetryB.pdf