Leonidas Alaoglu Memorial Lecture

Roughly speaking, a motive is a cohomology group of an algebraic variety, or more generally a diagram of algebraic varieties. Motives carry a great deal of interesting arithmetic structure: complex periods, l-adic galois representations, p-adic frobenius modules, etc. I will discuss a class of examples which include configuration spaces and motives associated to fundamental groups of algebraic varieties.

The discussion will focus on basic combinatorial properties, e.g. relations between Euler characteristics of motives and chromatic polynomials of graphs. I will also discuss periods; e.g. multiple zeta values, multiple polylogarithms, and multiple elliptic polylogarithms. Work of Ceyhan-Marcolli shows that Feynman amplitudes in position space are analogous to periods of such motives.

The talk will not use methods beyond elementary topology and complex manifold theory.