Dynamics of the product replacement algorithm

par Prof. Serge Cantat (University of Rennes)

jeudi 4 déc. 2025, 08:30 → 10:30 Europe/Paris

Thursday 4 December 2025, 4:30 PM - 6:30 PM (Korea)

Choose a compact Lie group G, say the group SO_k,  and an integer n > 2.
We will be interested in n-tuples (g₁,…, g_n) of elements in G and in the smallest closed subgroup containing such a tuple. The product replacement algorithm can be considered as a group action on Gⁿ generated by the following simple moves:

1. permuting the g_i,
2. changing one of them into its inverse,
3. changing some g_j into g_jg_i with i distinct from j.

Such ``moves’’ do not change the group generated by (g₁,…, g_n). The problem is to describe the orbits of the product replacement algorithm in Gⁿ. I will describe this problem and explain some results that hold when n is large (based on a joint work with C. Dupont and F. Martin-Baillon).

LINK FOR THE WEBINAR
https://univ-grenoble-alpes-fr.zoom.us/j/96099208605?pwd=bmExUGlIdEFBeVdVRW8rOFJuWkRpdz09