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

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Europe/Paris

Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

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.

Joint work with Andrew Soffer.

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