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Jun 18 2024

Dynamics Seminar: Distal actions of automorphisms on Lie groups G and Sub_G with applications to lattices, by Riddhi Shah

June 18, 2024

2:00 PM - 2:50 PM

Location

427 SEO

Address

Chicago, IL

Riddhi Shah (Jawaharlal Nehru University, New Delhi): Distal actions of automorphisms on Lie groups G and Sub_G with applications to lattices

On a locally compact group G, the space Sub_G of closed subgroups of G endowed with the Chabauty topology is compact. There is a natural action of the automorphism group Aut(G) on Sub_G. Distal maps were introduced by David Hilbert on compact spaces to study non-ergodic maps. After a gentle introduction to distal actions with some examples, we will discuss the distal actions of automorphisms on a connected Lie group G and Sub_G and characterise those acting distally on certain invariant subspaces of Sub_G for a large class of Lie groups. We will present a characterisation of the distal actions of automorphisms of a lattice L in G on Sub_L. We will also present a useful result on the structure of lattices in a connected Lie group.

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Contact

Alexander Furman

Date posted

Jun 13, 2024

Date updated

Jun 13, 2024

Speakers