Special Year 2016-17: Homological Mirror Symmetry

We'll discuss how dimensional reductions of the Haydys-Witten equations are connected to Haydys's definition of the Fukaya-Seidel category. Time permitting we'll touch on connections to Donaldson-Thomas's vision of higher-dimensional gauge theory.

I will discuss a construction of the homological mirror correspondence on algebraic integrable systems arising as moduli of flat bundles on curves. The focus will be on non-abelian Hodge theory as a tool for implementing hyper Kaehler rotations of...

Givental's quantization formula describes higher genus invariants from genus zero data, the Frobenius manifold. I will describe this quantization and state Teleman's result that this quantization actually describes all semisimple cohomological field...

In his 2005 paper "The Gromov-Witten potential associated to a TCFT" Kevin Costello described a procedure for recovering an analogue of the Gromov-Witten potential directly out of a cyclic A-inifinity algebra or category. Applying his construction...

In the first half of the talk I shall present a new algebraic proof of a result of Deligne-Illusie about the degeneration of the Hodge-de Rham spectral sequence. The idea is to reduce the main technical point of their proof to a question about the...

I will discuss a construction of the homological mirror correspondence on algebraic integrable systems arising as moduli of flat bundles on curves. The focus will be on non-abelian Hodge theory as a tool for implementing hyper Kaehler rotations of...

We'll talk about various dimensional reductions of the HW equations and the connections to (de)categorification as we continue explaining their physical origins. Time permitting we will discuss (conjectural?) relations to Fukaya-Seidel categories.

In this talk, we will discuss symplectomorphisms coming from Dehn twists along Lagrangian spherical manifolds. The main focus will be on the induced auto-equivalences of the Fukaya category. We will explain the auto-equivalence formula from several...