Yangyang Li
About
- I am an L.E. Dickson Instructor in the Department of Mathematics at the University of Chicago.
- I was a graduate student in the Department of Mathematics at Princeton University, supervised by Fernando Codá Marques
- Starting in Fall 2025, I will begin my appointment as a tenure-track Assistant Professor at the University of Notre Dame.
Email
- yangyangli [at] uchicago.edu
Research Interests
- Differential Geometry
- PDEs
Papers
- Existence of Infinitely Many Minimal Hypersurfaces in Higher-dimensional Closed Manifolds with Generic Metrics, Journal of Differential Geometry 124 (2) 381 - 395, June 2023 , arXiv:1901.08440 [Jan 2019]
- On the Existence of Minimal Hypersurfaces with Arbitrarily Large Area and Morse Index, Geometry & Topology 26 (6) 2713 - 2729, 2022 , arXiv:2001.07689 [Jan 2020]
- An Improved Morse Index Bound of Min-Max Minimal Hypersurfaces, Calculus of Variations and Partial Differential Equations 62, 179 (2023), arXiv:2007.14506 [Jul 2020]
- Generic Regularity of Minimal Hypersurfaces in Dimension 8 (joint with Zhihan Wang), arXiv:2012.05401 [Dec 2020] (superseded by arXiv:2205.01047)
- Equivariant manifolds with positive scalar curvature (joint with Tsz-Kiu Aaron Chow), Transactions of the American Mathematical Society 377 (2024), 5993-6020, arXiv:2109.12725 [Sep 2021]
- Minimal hypersurfaces for generic metrics in dimension 8 (joint with Zhihan Wang), accepted by Inventiones mathematicae, arXiv:2205.01047 [May 2022]
- A strong multiplicity one theorem in min-max theory (joint with Adrian C. Chu), arXiv:2309.07741 [Sep 2023]
- Existence of 5 minimal tori in 3-spheres of positive Ricci curvature (joint with Adrian C. Chu), arXiv:2409.09315 [Sep 2024]
(A summary of questions and results regarding enumeration of minimal submanifolds in spheres can be found Here)
- Existence and regularity of min-max anisotropic minimal hypersurfaces (joint with Guido De Philippis and Antonio De Rosa), arXiv:2409.15232 [Sep 2024]
- Non-persistence of strongly isolated singularities, and geometric applications (joint with Alessandro Carlotto and Zhihan Wang), arXiv:2411.12677 [Nov 2024]
Lecture Notes
- Introduction to Almgren-Pitts Min-max Theory (Notes for a 5-day minicourse given at Tsinghua University) Notes [July 2019]
Talks
- International geometric analysis conference in Milan, Bocconi University : TBD [June 2025]
- Simons Workshop on Geometric Analysis at Courant, NYU Courant : TBD [May 2025]
- Geometric Analysis seminar, Lehigh University : TBD [April 2025]
- Geometric Analysis Semina, UIUC : Existence of 5 minimal tori in 3-spheres of positive Ricci curvature [March 2025]
- Geometric Analysis Seminar, IMPA : Existence of 5 minimal tori in 3-spheres of positive Ricci curvature [March 2025]
- Analysis Seminar, Northwestern University : Non-persistence of Strongly Isolated Singularities and Hsiang’s minimal hyperspheres [February 2025]
- Analysis & PDE Seminar, John Hopkins University : Existence of 5 minimal tori in 3-spheres of positive Ricci curvature [Nov 2024]
- Workshop on Minimal Surfaces and Mean Curvature Flow 2024, BICMR : Existence and Regularity of Anisotropic Minimal Hypersurfaces [July 2024]
- CHallenge in ANalysis and GEometry, ETH Zurich : Existence and Regularity of Anisotropic Minimal Hypersurfaces [June 2024]
- Geometric Analysis Seminar, MIT : Existence and Regularity of Anisotropic Minimal Hypersurfaces [Mar 2024]
- Geometric Analysis and Topology Seminar, NYU Courant : Existence and Regularity of Anisotropic Minimal Hypersurfaces [Mar 2024]
- MAGEC 2024, Caltech : Existence and Regularity of Anisotropic Minimal Hypersurfaces [Mar 2024]
- Differential Geometry and Geometric Analysis seminar, Princeton University : Existence and Regularity of Anisotropic Minimal Hypersurfaces [Dec 2023]
- Geometric Analysis seminar, BICMR : Min-max widths of the unit 3-sphere and a strong multiplicity one theorem [Nov 2023]
- Geometric Analysis seminar, UTK : Min-max widths of the unit 3-sphere and a strong multiplicity one theorem [Oct 2023]
- BIRS-UBC-O Workshop, University of British Columbia : Existence and regularity of anisotropic minimal surfaces in Riemannian 3-manifolds [Aug 2023]
- Math Department Colloquium, Tsinghua University : The geometric structure of min-max minimal hypersurfaces [Jun 2023]
- Hua Loo-Keng Lecture Series, Chinese Academy of Sciences [Jun 2023]
- "Minimal surfaces in symmetric spaces" workshop, BIRS-IMAG: Existence and reguarity of anisotropic minimal surfaces [May 2023]
- Differential Geometry seminar, NCTS: Area ratio bounds and the existence of anisotropic minimal surfaces [Mar 2023]
- PDE and Differential Geometry seminar, UConn: Area ratio bounds and the existence of anisotropic minimal surfaces [Mar 2023]
- Geometry and Topology seminar, University of Toronto: Area ratio bounds and the existence of anisotropic minimal surfaces [Nov 2022]
- Joint Geometric Analysis Seminar, CUHK: Minimal hypersurfaces in a generic 8-dimensional closed manifold [Mar 2022]
- Geometric Analysis and Application seminar, Yale University: Minimal hypersurfaces in a generic 8-dimensional closed manifold [Feb 2022]
- Geometry and Topology seminar, University of Toronto: Minimal hypersurfaces in a generic 8-dimensional closed manifold [Nov 2021]
- Geometric Analysis Seminar, CUNY: Minimal hypersurfaces in a generic 8-dimensional closed manifold [Oct 2021]
- Analysis and Geometric Analysis Seminar, Cornell University: Minimal hypersurfaces in a generic 8-dimensional closed manifold [Oct 2021]
- Geometric Analysis Session, CMS 75th+1 Anniversary Summer Meeting: Generic Regularity of Minimal Hypersurfaces in Dimension 8 [Jun 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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