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I am a postdoctoral scholar in mathematics at Caltech, starting in 2026 Fall. My mentor is Prof. Antoine Song. I received my PhD in mathematics at Cornell University, supervised by Prof. Xin Zhou.
I got my BS in Mathematics (with Highest Honors) from UC Santa Barbara. My undergraduate advisor is Prof. Fedor Manin.
Research Interests
My research primarily lies in Differential Geometry and Geometric Analysis. During my PhD studies, I focused on adapting variants of Simon-Smith min-max theory to show the existence of minimal surfaces with controlled topological type in three-manifolds. In addition to min-max theory of minimal surfaces, my research interests include the theory of harmonic and p-harmonic maps, calibrated geometry, and their connections to representation theory.
Contact
Email: lxz833@caltech.edu
Address
Division of Physics, Mathematics, and Astronomy
California Institute of Technology
1200 E. California Boulevard, Pasadena, CA 91125
Academic Stuffs
Academic Stuffs
Preprints and Publications
Infinite existence of equivariant minimal hypersurfaces (with Tongrui Wang), arXiv:2604.13422
Area rigidity for the regular representation of surface groups (with Riccardo Caniato and Antoine Song), arXiv:2508.19480
Existence of embedded minimal tori in three-spheres with positive Ricci curvature (with Zhichao Wang), arXiv:2409.10391
Minimal surfaces with low genus in lens spaces (with Tongrui Wang and Xuan Yao), arXiv:2406.12584
J. reine angew. Math. 828 (2025), pp. 175-218
Generic scarring for minimal hypersurfaces in manifolds thick at infinity with a thin foliation at infinity, arXiv:2312.03591
Homological filling functions with coefficients (with Fedor Manin), arXiv:2009.13489
Groups Geom. Dyn. 16 (2022), no. 3, pp. 889–907
Lecture notes
Iteration methods in PDE and applications in geometry, Notes
A set of lecture notes on iteration methods in PDE and applications in geometry that Prof. Xin Zhou taught at Cornell in Fall 2024.
Lectures on min-max theory of minimal hypersurfaces, Notes
A set of lecture notes on the min-max theory of minimal hypersurfaces that Prof. Xin Zhou taught at Cornell in Fall 2022.
Academic Talks
Geometry Seminar, Rice University [Dec. 2026]
AMS Western Sectional Meeting, Arizona State University: “Existence of infinitely many minimal hypersurfaces in a fixed homology class.” [Nov. 2026]
Geometric Analysis Seminar, The University of Chicago: “Infinite existence of equivariant minimal hypersurfaces.” [Apr. 2026]
Geometric Analysis Seminar, The Chinese University of Hong Kong: “Area rigidity for the regular representation of surface groups.” [Jan. 2026]
Department Talk, Tsinghua University: “Area rigidity for the regular representation of surface groups.” [Dec. 2025]
Geometry & Topology Seminar, University of Toronto: “Area rigidity for the regular representation of surface groups.” [Nov. 2025]
Geometry Seminar, Lehigh University: “Embedded minimal tori in three-spheres.” [Sep. 2025]
Weyl Laws Across Mathematics Workshop, Brin MRC, University of Maryland: “Generic scarring for minimal hypersurfaces.” [May. 2025]
Geometry & Topology Seminar, Caltech: “Embedded minimal tori in three-spheres.” [Feb. 2025]
Geometric Analysis Seminar, Shanghai Jiao Tong University: “Embedded minimal tori in three-spheres.” [Jan. 2025]
Geometric Analysis Seminar, Brown University: “Embedded minimal tori in three-spheres.” [Nov. 2024]
Olivetti Club, Cornell University: “Minimal surfaces with low genus in lens spaces.” [Oct. 2024]
Student Geometry and Analysis Seminar (Zoom), University of Toronto: “Generic scarring for minimal hypersurfaces in manifolds thick at infinity with a thin foliation at infinity.” [Apr. 2024]
Geometric Analysis Seminar, Westlake University: “Generic scarring for minimal hypersurfaces in manifolds thick at infinity with a thin foliation at infinity.” [Jan. 2024]
Differential Geometry Seminar, Shanghai Center for Mathematical Sciences: “Generic scarring for minimal hypersurfaces in manifolds thick at infinity with a thin foliation at infinity.” [Dec. 2023]
Topology Seminar (Zoom), UC Santa Barbara: “Homological filling functions with coefficients.” [Dec. 2020]
Teaching
Instructor for Math 157a at Caltech: “Topics in Geometry and Topology: Characteristic Classes.” [2026 Fall]
TA for Math 4280 at Cornell: “Introduction to Partial Differential Equations.” [2026 Spring]
TA for Math 4540 at Cornell: “Introduction to Differential Geometry.” [2026 Spring]
TA for Math 4530 at Cornell: “Introduction to Topology.” [2025 Fall]
TA for Math 4130 at Cornell: “Honors Introduction to Analysis I.” [2025 Spring]
TA for Math 1920 at Cornell: “Multivariable Calculus for Engineers.” [2024 Fall]
Awards
2025 Inaugural Simons Dissertation Fellowship in Mathematics (provides research support to exceptional graduate students in mathematics).
2024 Robert J. Bättig Graduate Prize (for excellent research papers, and significant contributions).
2022 Mochizuki Memorial Fund Award (given annually to a graduating senior in mathematics for outstanding academic achievement).
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