Oscar Randal-Williams: Cohomology of moduli spaces: a case study

Talk at the "Mathematics Münster Mid-term Conference", 25-27 March 2024, in Münster, Germany. Abstract: Abstract: I will explain recent work of Bergström-Diaconu-Petersen-Westerland, and of Miller-Patzt-Petersen-R-W, which uses methods which have been developed over the last 25 years for studying the topology of certain moduli spaces in order to answer a question in arithmetic statistics (the function field analogue of a conjecture of Conrey-Farmer-Keating-Rubinstein-Snaith on moments of quadratic L-functions). My focus will be on the translation of this question to a problem in topology, and some of the modern methods which go into solving this problem.
More information on the conference: www.uni-muenst...