[Alta-Logic] Peripatetic Seminar November 20: Peter Zvengrowski

[Jonathan Gallagher]

Greetings,

We have a peripatetic seminar scheduled:
Speaker: Peter Zvengrowski
Location/Date: ICT 616/Tuesday Nov 20 @ 2 pm
Title: Goursat's Lemma with Relations to Geometry and Number Theory
Abstract:
Goursat's Lemma gives a description of the subgroups of the direct product
AxB of two groups, in terms of
subgroups of A and B. It originates in a paper written in 1889 by the famed
French analyst Edouard Goursat,
and was put into its modern form thanks to the work of two Canadian
mathematicians,  H.S.M. Coxeter and
J. Lambek. It can be generalized in several ways, one being to other
categories besides groups. Another
generalization is to studying the subgroups of AxBxC and higher direct
products, this turns out to be
surprisingly delicate and was done in joint work with Kristine Bauer and
Debasis Sen. This generalization
will be the main topic of the talk, and we shall also discuss applications
to various families of groups such
as abelian, finite, solvable, nilpotent, etc. In particular, the
application to cyclic groups involves some number
theory, such as the famed theorem of Dirichlet about primes in arithmetic
progressions.
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