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DTSTART;TZID=America/Los_Angeles:20240326T121500
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CREATED:20231215T050545Z
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UID:3331-1711455300-1711458600@colleges.claremont.edu
SUMMARY:Sublattices and subrings of Z^n and random finite abelian groups (Nathan Kaplan\, UC Irvine)
DESCRIPTION:How many sublattices of Zn have index at most X?  If we choose such a lattice L at random\, what is the probability that Zn/L is cyclic?  What is the probability that its order is odd?  Now let R be a random subring of Zn.  What is the probability that Zn/R is cyclic?  We will see how these questions fit into the study of random groups in number theory and combinatorics.  We will discuss connections to Cohen-Lenstra heuristics for class groups of number fields\, sandpile groups of random graphs\, and cokernels of random matrices over the integers.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-nathan-kaplan-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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