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Theta Functions for Log Calabi-Yau manifolds I -II

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

March 28, 2016 (02:30 PM PDT - 03:30 PM PDT)
Speaker(s): Sean Keel (University of Texas, Austin)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

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

Supplements
25687?type=thumb Keel Notes 463 KB application/pdf Download
Video/Audio Files

14478

H.264 Video 14478.mp4 357 MB video/mp4 rtsp://videos.msri.org/data/000/025/618/original/14478.mp4 Download
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