3:00–4:00 pm Eckhart Hall, Room 202
Title: Arithmetic Properties of Monodromy Representations of Families of Algebraic Varieties
Abstract: One broad goal of algebraic geometry is classifying algebraic varieties by the means of cohomological invariants attached to them. While being a seemingly more complicated question, it turns out that if one is rather interested in classifying families of algebraic varieties whose monodromy is large enough, the situation simplifies in several aspects, and there are results whose analogs for individual varieties are currently out of reach. I will describe current conjectural expectation for which monodromy representations arise from families of algebraic varieties, formulated in terms of the action of the absolute Galois group on the fundamental group of the base of the family, and what is presently known about it.