On the conjugacy problem in some matrix groups

par Adem Zeghib

lundi 16 mars 2026, 16:30 → 17:30 Europe/Paris

S435 (UMPA)

The conjugacy problem poses the following question : given two elements g,g' in a group G does there exist h in G such that g'=hgh^{-1}.  

It is dual to the centralizer problem, asking for generators of the centralizer of g.

In this talk, our focus will be on finitely generated matrix groups, tracing the historical development of the conjugacy problem in this specific context.

 

We will see how the structural solution for GL(n,ℤ) of Eick-Hoffman-O'Brien, together with an effective Tits alternative for the centralizer of a matrix, yield a practical algorithmic solution to the conjugacy problem in the symplectic group Sp(2n, ℤ).