Home /  Workshop /  Schedules /  Theta Functions for Log Calabi-Yau manifolds I -II

Theta Functions for Log Calabi-Yau manifolds I -II

Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016

March 29, 2016 (02:30 PM PDT - 03:30 PM PDT)
Speaker(s): Sean Keel (University of Texas, Austin)
Location: SLMath: Eisenbud Auditorium



In my two talks I'll explain the general features of my conjecture, joint with Gross, Hacking and Siebert, that the algebra of regular functions on an affine log CY (with maximal boundary), comes with a natural vector space basis, generalizing the characters of an algebraic torus, for which the structure constants for the multiplication rule are positive integers, counting holomorphic discs (on the mirror).

In particular, I'll explain how using these "theta functions" one can generalize the basic constructions of toric geometry. E.g. a single choice of anti-canonical normal crossing divisor on a Fano Y (conjecturally) canonically determines for each line bundle L on Y a basis of sections parameterized by the integer points of a "polytope" (more precisely, a piecewise integer affine  manifold with boundary).  The talks will be at a very general level -- in particular I won't assume any familiarity with cluster varieties or mirror symmetry

25690?type=thumb Keel Notes 404 KB application/pdf Download
Video/Audio Files


H.264 Video 14482.mp4 378 MB video/mp4 rtsp://videos.msri.org/data/000/025/625/original/14482.mp4 Download
Troubles with video?

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.