## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Spherical twists as derived flops

**Speaker:** Rina Anno

**Speaker Info:** Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

Spherical twists are autoequivalences of triangulated categories induced by so called spherical objects, or, more generally, by spherical functors. In the canonical example of the derived category of sheaves on a resolution of a Kleinian singularity spherical objects are the structure sheaves of the exceptional (-2)-curves, and the corresponding twists generate a braid group action. By viewing the structure sheaves instead of the curves themselves we untie this construction from the explicit geometry and make it work in the derived category of sheaves. We can go even further. Kontsevich's homological mirror symmetry proposes that there are families of "homological mirror" equivalent varieties with the same derived category of sheaves, related by birational transformations in codimension 2 called flops. I will explain how one can stripe certain Mukai flops from their geometric definition and see a network that expands the braid group action by spherical twists to some discrete category action.

**Date:** Thursday, January 20, 2011

**Time:** 3:00pm

**Where:** Lunt 107

**Contact Person:** Jesse Wolfson

**Contact email:** wolfson@math.northwestern.edu

**Contact Phone:**

Copyright © 1997-2024
Department of Mathematics, Northwestern University.