Event

Talk
Canonical Coordinates
Prof. Dr. Sean Keel
2 Jul 2013, 17:45 – 18:45

Prof. Dr. Sean Keel will discuss his conjecture, joint with Gross and Hacking, that affine Calabi-Yau manifolds (with maximal boundary) have canonical "theta functions" -- a canonical vector space basis of the algebra of global functions, with structure constants for the multiplication rule, non-negative integers determined by counts of rational curves
(on the mirror), and our partial results, which include a proof in dimension two, and a proof, joint with Kontsevich, of much of the conjecture for cluster varieties. We obtain in particular in a unified way

1) the classical theory of theta functions for elliptic curves
2) the natural trace functions on the SL2 character variety of a punctured riemann surface
3) a canonical basis for each irreducible representation of SLr
4) a canonical basis for loads of cluster algebras

by a general, and conceptually quite simple, scheme that applies to any CY, and which in particular does not involve any elliptic curves, riemann surfaces, representation theory, or cluster algebras. He will aim the talk at a quite broad mathematical audience -- if you know what is meant by the order of pole of a rational function along a divisor in an algebraic variety then you know more than enough to absorb the main ideas.

http://www.ma.utexas.edu/users/keel/

Related to:

• Sean Keel
• [C1] Algebraic Topology: Rigidity and Dynamics