# Yangyang Li

### About

*Photo credit to* Summer Chen
- I am currently a fifth-year PhD student at the Department of Mathematics, Princeton University
- My advisor is Fernando Codá Marques

### Email

- yl15 [at] math.princeton.edu

### Research Interests

- Differential Geometry
- PDEs

### Papers

*Existence of Infinitely Many Minimal Hypersurfaces in Higher-dimensional Closed Manifolds with Generic Metrics*, Accepted by **Journal of Differential Geometry**, arXiv:1901.08440 [Jan 2019]
*On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index*, Accepted by **Geometry & Topology**, arXiv:2001.07689 [Jan 2020]
*An Improved Morse Index Bound of Min-Max Minimal Hypersurfaces*, arXiv:2007. [July 2020]
*Generic Regularity of Minimal Hypersurfaces in Dimension 8* (joint with Zhihan Wang), arXiv:2012.05401 [Dec 2020]
*Equivariant manifolds with positive scalar curvature* (joint with Tsz-Kiu Aaron Chow), arXiv:2109.12725 [Sept 2021]

### Lecture Notes

*Introduction to Almgren-Pitts Min-max Theory* (Notes for a 5-day minicourse given at Tsinghua University) Notes [July 2019]

### Talks

- Geometry and Topology seminar,
** University of Toronto **: TBA [Nov 2021]
- Geometric Analysis Seminar,
** CUNY**: TBA [Oct 2021]
- Analysis and Geometric Analysis Seminar,
** Cornell University**: TBA [Oct 2021]
- Geometric Analysis Session,
**CMS 75th+1 Anniversary Summer Meeting**: *Generic Regularity of Minimal Hypersurfaces in Dimension 8* [June 2021]
- Geometric Analysis Seminar,
**University of Chicago**: *Generic Regularity of Minimal Hypersurfaces in Dimension 8* [May 2021] (Slides)
- Differential Geometry Seminar,
**UC San Diego**: *Generic Regularity of Minimal Hypersurfaces in Dimension 8* [Apr 2021]
- The 1st Geometric Analysis Festival:
*Generic Regularity of Minimal Hypersurfaces in Dimension 8* [Feb 2021] (Video)
- Analysis and Partial Differential Equations Seminar,
**John Hopkins University**: *Generic Regularity of Minimal Hypersurfaces in Dimension 8* [Nov 2020]
- Special Session on Variational Aspects of Geometric Analysis,
**AMS Meeting**: *Min-max minimal hypersurfaces in higher dimensions* [Oct 2020]
- Geometry Seminar,
**Stanford University**: *Existence of minimal hypersurfaces with arbitrarily large area and Morse index* [May 2020]
- Differential Geometry Seminar,
**UC Santa Barbra**: *Existence of minimal hypersurfaces with arbitrarily large area and Morse index* [Mar 2020]
- Geometric Analysis Learning Seminar,
**Princeton University**: *Minimal Hypersurfaces for Generic Metrics and Yau's Conjecture* [Mar 2019]
- Graduate Student Seminar,
**Princeton University**: *Positive Mass Theorem* [Oct 2017]

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