##### Department of Mathematics,

University of California San Diego

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### Group Actions Seminar

## Minju Lee - Graduate student

#### Yale University

## Invariant measures for horospherical actions and Anosov groups

##### Abstract:

Let $\Gamma$ be an Anosov subgroup of a connected semisimple real linear Lie group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $\Gamma \backslash G$, up to proportionality, is homeomorphic to $\mathbb{R}^{\mathrm{rank} (G)-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup which normalizes $N$. \\ \\ This is joint work with Hee Oh.

Host: Amir Mohammadi

### January 12, 2021

### 9:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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