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DTSTAMP:20210927T181607
DTSTART;TZID=America/Detroit:20210927T150000
DTEND;TZID=America/Detroit:20210927T160000
SUMMARY:Workshop / Seminar:RTG Seminar on Number Theory Seminar
DESCRIPTION: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 finite-cardinality R-modules under the 1/#Aut weighting. They defined a \"zeta\" function \sum_M 1/#Aut(M) |M|^{-s} summing over all finite-cardinality R-modules\, and they showed that it is an infinite product involving the Dedekind zeta function of R. In this talk\, we discuss this Cohen--Lenstra 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 q-series\, which we will describe in more detail. Speaker(s): Yifeng Huang (University of Michigan)
UID:85270-21626132@events.umich.edu
URL:https://events.umich.edu/event/85270
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4088
CONTACT:
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