Homological Mirror Symmetry

In the two talks, aimed at a broad mathematical audience, I'll explain my conjecture, joint with Gross, Hacking, and Siebert, which says, informally, that if you live on a Calabi Yau, your world comes with an intrinsic global positioning system...

In the two talks, aimed at a broad mathematical audience, I'll explain my conjecture, joint with Gross, Hacking, and Siebert, which says, informally, that if you live on a Calabi Yau, your world comes with an intrinsic global positioning system...

I will explain the case of log Calabi-Yau surfaces, based on my previous works and my work in progress with Sean Keel.

I will explain the construction and the geometry of the non-archimedean SYZ fibration.

Continuation of Friday, Feb 3 minicourse. We will discuss a notion of noncommutative and derived algebraic variety. This approach comes from a generalization of derived categories (quasi) coherent sheaves on usual algebraic varieties and their...

We are will discuss a notion of noncommutative and derived algebraic variety. This approach comes from a generalization of derived categories of (quasi)coherent sheaves on usual algebraic varieties and their enhancements. We are going to talk about...

We are will discuss a notion of noncommutative and derived algebraic variety. This approach comes from a generalization of derived categories of (quasi)coherent sheaves on usual algebraic varieties and their enhancements. We are going to talk about...

I will survey the coherent-constructible correspondence of Bondal, which embeds the derived category of coherent sheaves on a toric variety into the derived category of constructible sheaves on a compact torus. The tools of the first lecture turn...

I will give an introduction to the microlocal theory of sheaves after Kashiwara and Schapira, and some of its recent applications in symplectic topology. I'll start with the basics, but target applications for the 75 minutes are Tamarkin's proof of...

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open...