Embedded Files
At the Big Island, Hawaii, by Hongjie Zeng.
About Me
About Me
I am Yusen Xia (in Chinese: 夏雨森). I’m a 6th year PhD student at Mathematics Department, UC Santa Barbara (fortunately advised by Prof Guofang Wei).
I am on the 2026–27 job market for postdoctoral positions.
I got my BSc in Mathematics degree (with First Class honors) from Hong Kong University of Science & Technology (HKUST). I was an exchange student at UCLA from Winter to Spring 2020.
Research Interest
Research Interest
My research lies in geometric analysis, with a focus on eigenvalue and eigenfunction problems on Riemannian manifolds and domains. My current work concerns Neumann eigenvalues of geodesic triangles in space forms and log-concavity phenomena for first Dirichlet eigenfunctions on positively curved manifolds.
I am also broadly interested in differential geometry and geometric-PDE problems arising in geometry.
Contact:
Contact:
Email: yusen (AT) ucsb (DOT) edu
Address
Address
Department of Mathematics, University of California, Santa Barbara
552 University Rd, South Hall, Santa Barbara, CA 93106
Preprints & Publications
Preprints & Publications
Log-Concavity of First Dirichlet Eigenfunctions on CP^2, Preprint, 2026.
A Sharp Diameter-Dependent Lower Bound for the First Nonzero Neumann Eigenvalue of Geodesic Triangles in Space Forms, with Shoo Seto & Guofang Wei, submitted, 2026
On the PPW Conjecture for Hopf-Symmetric Sets in Non-compact Rank One Symmetric Space, J. Geom. Anal., 2026
Invited Research Talks
Invited Research Talks
Upcoming:
Geometry and Analysis Seminar, UC Santa Cruz, Dec 2026
Geometry Seminar, Syracuse University, Nov 2026
AMS Western Sectional Meeting, Special Session on Geometric Analysis, Nov 2026
Geometry Seminar, Indiana University, Bloomington, Oct 2026
The Illinois Geometric Analysis Seminar, University of Illinois Urbana–Champaign, Oct 2026
Harmonic Analysis and Differential Equations Seminar, University of Illinois Urbana–Champaign, Oct 2026
Differential Geometry Seminar, University of California, Irvine, Oct 2026
Differential Geometry Seminar, University of California, Santa Barbara, Oct 2026
Geometry and Topology Seminar, University of California, Riverside, May 2026
Soul and Shape: Metric Structures and Geometric Analysis, Lightning talk, University of Oklahoma, Apr 2026
AMS Western Sectional Meeting, Special Session on Recent developments in geometric analysis, Mar 2026
Pure Math Seminar, Hong Kong University of Science and Technology, Jul 2025
Differential Geometry Seminar, University of California, Santa Barbara, Apr 2025
Page updated
Google Sites
Report abuse