Date: September 18, 2014

Time: 11:00AM - 12:00PM

Location: BLOC 220

Speaker: Sean Keel, U Texas

  

Title: Theta functions, Canonical Bases, and Moduli of Calabi-Yaus, III

Abstract: In my second and third talks, where I will assume some (but not much) familiarity with algebraic geometry, I will explain the mirror symmetric ideas behind the construction, focusing on the simpler case of open Calabi-Yau, and in particular, cluster, varieties. Our main theorem (joint with Kontsevich) is (roughly) that if an affine Calabi-Yau variety U has a Zariski open cover by algebraic tori, then the algebra O(U) of regular functions has a canonical vector space basis. The theorem, and proof, has many interesting applications. E.g. it produces a vector space basis for each irreducible representation of a semi-simple Lie group G canonically determined by a choice of H \subset B \subset G (a maximal torus in a Borel in G), by a construction that involves no representation theory (just the fact that U = the associated open double Bruhat cell is a CY of the right sort).

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