Paul Johnson
Title: Hurwitz numbers and moduli spaces of curves"
Abstract: Hurwitz numbers count covers of curves with specified ramification. Hurwitz numbers can also be interpreted in terms of group theory or graphs on surfaces, and these disparate viewpoints mean Hurwitz theory arises in many different contexts. We'll give something of a survey of Hurwitz numbers, with a focus on ``ELSV-type formulas", which express intersection numbers on moduli spaces of curves with some extra structure in terms of Hurwitz numbers.