Back to Departmental Colloquium: Fall 2011
Departmental Colloquium
Date: Thursday, Oct 27, 2011
Time: 4:15PM
Location: JWB 335
Andrei Caldararu
University of Wisconsin, Madison
Title |
The Pfaffian-Grassmannian derived equivalence |
Abstract |
String theory relates certain seemingly different manifolds through a relationship called mirror symmetry. Discovered about 25 years ago, this story is still very mysterious from a mathematical point of view. Despite the name, mirror symmetry is not entirely symmetric – several distinct spaces can be mirrors to a given one. When this happens it is expected that certain invariants of these “double mirrors” match up. For a long time the only known examples of double mirrors arose through a simple construction called a flop, which led to the conjecture that this would be a general phenomenon. In joint work with Lev Borisov we constructed the first counterexample to this, which I shall present. Explicitly, I shall construct two Calabi-Yau threefolds which are not related by flops, but are derived equivalent, and therefore are expected to arise through a double mirror construction. The talk will be accessible to a wide audience, in particular to graduate students. There will even be several pictures! |
Commutative Algebra
Topology