SPEAKERUli Walther б¡]Purdue University^

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.