### Heat kernel pull back metrics, non-collapsed spaces and convexity

- Series
- Dissertation Defense
- Time
- Friday, April 1, 2022 - 13:00 for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Xingyu Zhu – Georgia Tech – xyzhu@gatech.edu

We present in this talk some results concerning the metric measure spaces with lower Ricci curvature bounds.

Firstly, we extend the technique of smoothing Riemannian metric by heat kernel pull back metrics to non-compact setting, and use it to solve a conjecture of De Philippis-Gigli. This is joint work with Brena-Gigli-Honda. Secondly, we study the second term in the short time expansion of the heat kernel pull back metrics and the connection with non-collapsed spaces. This is joint work with Honda. Finally, we use the 1D localization technique to extend some convexity results on the regular set and in the interior of such metric measure spaces.

Link: https://gatech.zoom.us/j/5491403383?pwd=Um1NM05MeWJMRnNuVHViQ1NWdHFaZz09