Dynamics Seminar
Riddhi Shah
Jawaharlal Nehru University, New Delhi
Distal actions of automorphisms on Lie groups G and Sub_G with applications to lattices
Abstract: 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.
Tuesday June 18, 2024 at 2:00 PM in 427 SEO