Wednesday, March 28th, 2018
12:00 pm - 1:00 pm, in Science 2-063

Gabriel Kerr

Kansas State University

Decompositions of algebras, categories and spaces - A (bi)rational approach to mirror symmetry

Abstract: Early theorems in algebra, such as Jordan-Holder decomposition, provide ways of breaking down complicated structures into elementary, or at least more fundamental, instances. Analogs of such a decomposition occur in more advanced contexts, and in this talk I will explain how they arise in one version of mirror symmetry. Mirror symmetry relates invariants of the algebraic geometry of a variety X to invariants of the symplectic geometry of a mirror manifold Y along with a potential function W. In algebraic geometry, one may adopt a birational approach and consider a minimal model sequence starting at X and ending in a minimal model. In a concrete sense, such a sequence can be considered as a decomposition of your original space X. Likewise, for the symplectic mirror, one may degenerate Y and its potential, resulting in an actual decomposition of Y into a sequence of contact cobordisms. I will describe how such decompositions come in mirror pairs and discuss their categorical incarnations in homological mirror symmetry.