Theta Functions for Log CalabiYau manifolds I II
Hot Topics: Cluster algebras and wallcrossing March 28, 2016  April 01, 2016
Location: SLMath: Eisenbud Auditorium
canonical divisors
log forms
log CalabiYau varieties
special functions
theta functions
mirror symmetry
13P10  Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14K20  Analytic theory of abelian varieties; abelian integrals and differentials
14K22  Complex multiplication and abelian varieties [See also 11G15]
14J50  Automorphisms of surfaces and higherdimensional varieties
14482
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 anticanonical 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
Keel Notes

Download 
14482
H.264 Video 
14482.mp4

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.