##### Department of Mathematics,

University of California San Diego

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### Math 211 B00 - Group Actions Seminar

## Wooyeon Kim

#### ETH Zurich

## Effective equidistribution of expanding translates in $ASL_d(\mathbb{R})/ASL_d(\mathbb{Z})$

##### Abstract:

In this talk, we discuss effective versions of Ratnerâ€™s theorems in the space of affine lattices. For $d \geq 2$, let $Y=ASL_d(\mathbb{R})/ASL_d(\mathbb{Z})$, $H$ be a minimal horospherical group of $SL_d(\mathbb{R})$ embedded in $ASL_d(\mathbb{R})$, and $a_t$ be the corresponding diagonal flow. Then $(a_t)$-push-forwards of a piece of $H$-orbit become equidistributed with a polynomial error rate under certain Diophantine condition of the initial point of the orbit. This generalizes the previous results of StrÃ¶mbergsson for $d = 2$ and of Prinyasart for $d = 3$.

Host: Brandon Seward

### October 28, 2021

### 12:00 PM

Zoom ID 967 4109 3409 (email an organizer for the password)

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