Computing homology of the (unordered) configuration space of fixed number of points on a topological space is a classical problem in topology, going all the way back to V.I. Arnol'd and his students in 1970's. In this talk, we will first briefly discuss some known results mainly focusing on the case when the given topological space is an orientable manifold. Then we will see how to relate the Euler characteristics of the configuration spaces to that of the symmetric powers, mainly using combinatorial ideas given by R. Vakil and M.M. Wood about motivic zeta function of an algebraic variety.

If time permits, we will discuss what are the limitations of the zeta function method and try to come up with some sounding conjectures together. This talk will be extremely elementary, so whomever taken introductory algebra and topology courses should be able to follow. Speaker(s): Gilyoung Cheong (University of Michigan)