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Homotopy Theory Seminar

Thursday, October 27, 2022 - 3:30pm

Anh Hoang Trong Nam

University of Minnesota


University of Pennsylvania

In the last dozen years, topological methods have been shown to produce a new pathway to study arithmetic statistics over function fields, most notably in Ellenberg-Venkatesh-Westerland's work on the Cohen-Lenstra heuristics. More recently, Ellenberg, Tran and Westerland proved the upper bound in Malle's conjecture over function fields by employing a topological observation which identifies the homology of the braid groups with coefficients arising from braided vector spaces with the cohomology of a quantum shuffle algebra, using the Fox-Neuwirth cellular stratification of configuration spaces of the plane. In this talk, we will extend their techniques to study configuration spaces of the punctured plane and prove a similar result for the homology of the Artin groups of type B. As an application, we will discuss computations when the braid representations are one-dimensional over a field, which shed light on a special case of a conjecture about the homology of mixed braid groups due to Ellenberg-Kim-Shusterman.