# Algebraic Geometry Seminar

#### Intersections of two Grassmannians in P^9

**Speaker:**
Alexander Perry, Columbia University

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, October 10, 2017, 3:30 p.m.

**Synopsis:**

I will discuss the intersection of two copies of Gr(2,5) embedded in P^9, and the intersection of the two projectively dual Grassmannians in the dual projective space. These intersections are deformation equivalent Calabi-Yau threefolds. I will explain why they are derived equivalent but generically not birational, and use this to obtain a counterexample to the birational Torelli problem for Calabi-Yau threefolds, as well as new examples of zero divisors in the Grothendieck ring of varieties. This is joint work with Lev Borisov and Andrei Caldararu.