Number Theory Seminar
Derek Garton
Northwestern University
Random matrices and the Cohen-Lenstra-Martinet heuristics
Abstract: The Cohen-Lenstra-Martinet heuristics predict the frequency with
which a fixed finite abelian group appears as an ideal class group of an
extension of number fields, for certain sets of extensions of a base
field. Recently, Malle found numerical evidence suggesting that their
proposed frequency is incorrect when there are unexpected roots of unity
in the base field of these extensions. Moreover, Malle proposed a new
frequency, which is a much better match for his data. I will explain a
random matrix heuristic (coming from function fields) that leads to a
function field version of Malle's conjecture (as well as generalizations
of it).
Tuesday March 12, 2013 at 1:00 PM in SEO 636