Geometry and Topology Seminar: Patterson-Sullivan measures for relative Anosov groups

Speaker: Tengren Zhang (National University of Singapore)

Abstract: Relative Anosov groups are a class of subgroups of a semisimple Lie group G that include all Anosov subgroups, and all geometrically finite subgroups when G has rank one. We prove that under some mild conditions on G, the Poincare series associated to a relative Anosov subgroup (and a linear function on the Cartan subspace of G) diverges at its critical exponent if its critical exponent is finite. As a consequence of this, we deduce uniqueness and ergodicity results for the associated Patterson-Sullivan measure whose dimension is the critical exponent. This is joint work with Richard Canary and Andrew Zimmer.

Time: 4pm, Friday, Nov. 29, 2024

Zoom Meeting No.: 942 4677 6586 (Passcode 451690)