# Mathematics Colloquium

#### Collapsing of the Kahler-Ricci flow and of hyperkahler manifolds

**Speaker:**
Valentino Tosatti, Northwestern

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, April 8, 2019, 3:45 p.m.

**Synopsis:**

I will explain the conjectural picture of the behavior of the Ricci flow on compact Kahler manifolds of arbitrary dimension, originating from work of Song and Tian, and discuss some recent progress towards establishing this picture, including finite-time singularities as well as long-time collapsing behavior. I will also explain how the techniques we introduced to study these problems can be used to study the collapsing of hyperkahler manifolds, and establish a conjecture of Gross-Wilson and Kontsevich-Soibelman coming from the Strominger-Yau-Zaslow picture of mirror symmetry for these spaces.