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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

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