Geometry seminar

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16 September 2026
15:30-16:30

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kein Seminar

23 September 2026
15:30-16:30

Segev Gonen Cohen
ETH Zurich, Switzerland

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Title	Actions of lattices on manifolds
Speaker, Affiliation	Segev Gonen Cohen, ETH Zurich, Switzerland
Date, Time	23 September 2026, 15:30-16:30
Location	HG G 43
Abstract	In this talk we describe recent progress on the Zimmer Programme, the study of actions of lattices in Lie groups on manifolds by diffeomorphisms. We begin by recalling motivations and some important examples, explain the general strategy introduced by Brown-Fisher-Hurtado when the manifold is of low enough dimension, and discuss modifications that allow us to prove results in more general semisimple and S-arithmetic groups. Time willing, we will also describe some recent progress on actions of dense subgroups of Lie groups on manifolds.

Actions of lattices on manifoldsread_more

30 September 2026
15:30-16:30

Serge Cantat
Université de Rennes

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Title	On the product replacement algorithm in compact Lie groups
Speaker, Affiliation	Serge Cantat, Université de Rennes
Date, Time	30 September 2026, 15:30-16:30
Location	HG G 43
Abstract	Let G be a compact Lie group. Let n be an integer. Given n elements g₁, …, g_n in G, one can choose one of the g_i and replace it into its inverse, or into the product g_ig_j for some j distinct from i; these basic operations do not change the subgroup of G generated by the g_i. Doing so, one gets a group of transformations of Gⁿ (generated by all these basic operations). The problem I will discuss is: what can be said on the dynamics of this group action on Gⁿ? For instance, can we describe the closures of orbits, or the invariant probability measures? As we shall see, the answer is yes when n becomes large, in fact larger than an explicit constant that depends on G. This is based on a joint work with Christophe Dupont and Florestan Martin-Baillon, which complements previous works of Tsachik Gelander.