NTS Fall 2012/Abstracts

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September 13

Nigel Boston (UW–Madison)
Title: Non-abelian Cohen–Lenstra heuristics

Abstract: In 1983, Cohen and Lenstra observed that the frequency with which a given abelian p-group A (p odd) arises as the p-class group of an imaginary quadratic field K is apparently proportional to 1/|Aut(A)|. The group A is isomorphic to the Galois group of the maximal unramified abelian p-extension of K. In work with Michael Bush and Farshid Hajir, I generalized this to non-abelian unramified p-extensions of imaginary quadratic fields. I shall recall all the above and describe a further generalization to non-abelian unramified p-extensions of H-extensions of Q, for any p, H, where p does not divide the order of H.

September 20

Who? (Where?)
Title: Multiplicities of automorphic forms on GL2

Abstract: I will discuss some ideas related to the theory of p-adically completed cohomology developed by Frank Calegari and Matthew Emerton. If F is a number field which is not totally real, I will use these ideas to prove a strong upper bound for the dimension of the space of cohomological automorphic forms on GL2 over F which have fixed level and growing weight.

September 27

Jordan Ellenberg (UW–Madison)
Title: tba

Abstract: tba

Organizer contact information

Robert Harron

Zev Klagsbrun

Sean Rostami

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