High dimensional cohomology of moduli spaces

The conference will focus on connections and analogies between the cohomology of geometric moduli spaces (e.g. the moduli spaces of Riemann surfaces, or graphs), and the cohomology of arithmetic groups (what might be called “algebraic moduli spaces”). Such analogies have been pursued since the 1980’s, but new tools and perspectives (tropical geometry, graph homology) have recently been brought to the subject. This has established much more direct links between both worlds, and led to a flurry of new results. Our primary focus will be to investigate what happens far outside the stable range, where very little is currently known. We will also explore the relationship between these objects and other topics, such as Steinberg modules, algebraic K-theory, and the theory of multiple polylogarithms.