Algebraic Geometry Seminar

DATE2019-01-08 11:10-12:00


SPEAKERUli Walther 教授(Purdue University

TITLE Feynman Diagrams and Singularities of Configuration Polynomials

ABSTRACT A Feynman diagram is a graph with some extra decorations. It contains in condensed form the information necessary to describe a particle interaction and the corresponding Feynman integral. This integral involves a polynomial that appears (with some power) as denominator of the integrand. Understanding the singularities of this graph polynomial is crucial for evaluating the integrals (which, apart from their physical nature also exhibit some mysterious connection to number theory). We discuss a classica, more general, approach via matroids that leads to configuration polynomials. We then discuss the structure of the singular locus of graph and configuration polynomials. This is joint work with Graham Denham and Mathias Schulze. No knowledge of Feynman diagrams is assumed. The talk is intended to be elementary and suitable for students.