|Algebraic Geometry Seminar, Purdue University, Prof. Uli Walther |
Tuesday, January 8, 11:10—12:00 數學系3樓會議室
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.
|Colloquium, Purdue University, Prof. Uli Walther |
Thursday, January 10, 15:10—16:00 數學系3174
Title:What is...the Monodromy Conjecture?
Abstract: Suppose f is a polynomial in n variables whose coefficients are integers. In this mostly expository talk we discuss 4 classical ways (differential, geometric, topological, and arithmetic in nature) that lead to four single variable expressions derived from f that measure its singularities. These are the Bernstein-Sato polynomial, the monodromy on the Milnor fiber, the topological zeta function an the Igusa zeta function. We explain some known relations between these and then discuss a conjecture that has been open for 30 years. The talk is intended to be elementary and suitable for students.