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Sublattices and subrings of Z^n and random finite abelian groups (Nathan Kaplan, UC Irvine)

March 26 @ 12:15 pm - 1:10 pm

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.


March 26
12:15 pm - 1:10 pm
Event Category:


Estella 2099