Horospherically Invariant Measures and Rank Dichotomy for Anosov Groups - Lecture 2

Explore a 57-minute lecture on horospherically invariant measures and rank dichotomy for Anosov groups. Delve into the work of Minju Lee from the University of Chicago, presented at the Institut des Hautes Etudes Scientifiques (IHES). Examine the existence of at most one N-invariant measure in Γ\G supported on the forward recurrent subset for the exp(tu)-action, where G is a product of simple real algebraic groups of rank one and Γ is a Zariski dense and Anosov subgroup. Investigate this generalization of unique ergodicity results for horospherical action, building upon the work of Furstenberg, Burger, Roblin, and Winter for Γ convex cocompact. Learn about ergodic measures, measure rigidity, directionally recurrent sets, Burger-Roblin measures, and ergodic theorems. Gain insights into the proof scheme, including local estimates, in this collaborative research with Or Landesberg, Elon Lindenstrauss, and Hee Oh.

Intro
Ergodic measures for horospherical action
Measure rigidity (r: Lattice)
Measure rigidity (r: Geom. infinite)
Directionally recurrent set
Burger-Roblin measures
Ergodic theorems
Scheme of the proof
1. Local estimate