"Our aim is to provide a platform for exchanging ideas and recent results on algebraic transformation groups. The seminar brings together mathematicians worldwide and is particularly suitable for graduate students and researchers in algebraic geometry."
🗓️ PERIODICITY: Monthly, first Monday
🕒 TIME: 16:00 - Paris Time
⏳ DURATION: 60 minutes per talk
🔗 PLATFORM: ZOOM
2025-11-03 at 15:00 Paris Time — Serge Cantat (CNRS, Universite de Rennes)
Abstract: Choose a compact Lie group G, say the group SO_k, and an integer n > 2. We will be interested in n-tuples (g_1, …, 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 G^n generated by the following simple moves:
(a) permuting the g_i,
(b) changing one of them into its inverse, and
(c) changing some g_j into g_jg_i with i distinct from j.
Such ``moves’’ do not change the group generated by (g_1, …, g_n). The problem is to describe the orbits of the product replacement algorithm in G^n. 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).
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