Higman’s conjecture on the number of conjugacy classes of U(n,q)

par Prof. Igor PAK (UCLA)

jeudi 21 août 2014, 13:00 → 15:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

In 1960, Higman asked whether the number f(n,q) of conjugacy classes of n x n unitriangular matrices U(n,q) over the finite field with q elements, is polynomial in q for every n.  I will survey what is known about this problem, explain the connections to realization spaces of matroids, enumerative combinatorics and group representation theory.  I will then describe our recent efforts to prove the conjecture for small n and disprove it for large n.

Joint work with Andrew Soffer.