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.
This video was produced by the University of Münster, as part of the workshop Mathematics Münster Mid-term Conference.
