Date: Monday, September 27, 2021
Location: 4088 East Hall (3:00 PM to 4:00 PM)
Title: A generalization of a zeta function of CohenLenstra
Abstract: In the famous 1983 paper, when studying the heuristic distribution of class groups of imaginary quadratic fields, Cohen and Lenstra considered the weighting of a finite abelian group G with a weight proportional to 1/#Aut(G). More generally, for a given Dedekind domain R, they studied the statistics of finitecardinality Rmodules under the 1/#Aut weighting. They defined a "zeta" function \sum_M 1/#Aut(M) M^{s} summing over all finitecardinality Rmodules, and they showed that it is an infinite product involving the Dedekind zeta function of R. In this talk, we discuss this CohenLenstra zeta function defined for other families of rings, where the known results are organized in terms of the Krull dimension. The "nodal singularity" R=Fq[u,v]/(uv) is a surprisingly interesting example that gives rise to a peculiar qseries, which we will describe in more detail.
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Speaker: Yifeng Huang
Institution: University of Michigan
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