Abstract: We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. In particular, we obtain an effective closing lemma on  $\mathcal{H}(2)$, a result that has been studied extensively in homogeneous dynamics. The proofs make use of spectral gaps, and of the classification of Teichm\"{u}ller curves in $\mathcal{H}(2)$. This is based on the joint work with Pengyu Yang.

The seminar will also be livestreamed via Tencent Meeting.
https://meeting.tencent.com/dm/m7VqKgGN8RWq
Meeting number: 389-817-010
Password: 240408

The seminar will start at 2pm instead of the usual 3pm.