Rice University Department of Mathematics Colloquium

Mirror symmetry for affine varieties via geometric topology and Legendrian knot theory

4:00 pm Thursday, September 15th, 2016
Emmy Murphy (MIT)

Abstract: Pretty scary title, but the talk will be accessible for a general audience. Mirror symmetry is something of a large and impenetrable theory coming from mathematical physics, which is some sort of duality between complex algebraic geometry and symplectic geometry. Currently we don't have a completely clear understanding of why this phenomenon occurs, and there are dozens of perspectives of how to view mirror symmetry. Part of the mystery stems from the fact that in order to see mirror symmetry even in fixed examples, you need to have a very thorough understanding of the symplectic manifold in question: essentially understanding all pseudo-holomorphic curves with boundaries on all possible Lagrangian submanifolds. For this reason, most approaches to mirror symmetry focus on manifolds with large symmetry actions, and everything reduces to the algebra of the symmetry group. This talk will focus on the opposite approach: you understand the manifold from a topologist's perspective, as a Legendrian handlebody, and once you have a picture of the manifold's structure you can play with it, simplify it, and eventually see all the algebra of mirror symmetry visually.

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