Geometry Seminar

Date: April 8, 2019

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Bernd Siebert, University of Texas

Title: Toric degenerations - a finite element method in algebraic geometry

Abstract: Toric degenerations in the broad sense referred to here, are deformations with central fiber a union of toric varieties, intersecting pairwise along joint toric divisors. A typical example is a family of quartic hypersurfaces in projective 3-space with central fiber the union of four coordinate hyperplanes. The interesting thing about such degenerations is that there is a large class of examples that can be produced canonically out of discrete data, thus giving a vast generalization of toric geometry (joint work with Mark Gross). In the talk I will give an overview of such degenerations, the relation to tropical geometry and wall structures, the explanation of the mirror phenomenon in this framework and the appearance of special functions generalizing Riemannian theta functions.