About me.
I started my undergraduate study in 2013 at School of Mathematical Science, Nankai University, Tianjin, China.
I ontained my Ph. D. degree at University of California, Santa Barbara in 2022. My advisor is Xianzhe Dai.
I was a postdoctoral fellow at Beijing International Center for Mathematical Research (BICMR), Peking University, under the supervision of Xiaobo Liu.
I am curretnly a postdoc at Northeastern University under the supervision of Maxim Braverman.
Email Address
Curriculum Vitae
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Research Statement
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Besides mathematics, I enjoy playing the card game Yu-Gi-Oh , cycling and swimming.
Research
My main interests are geometric analysis and PDEs. More concretely, my current research focuses on the geometry and topology of the Landau-Ginzburg (LG) models, gluing formula of global spectral invariants and comparison geometry of hypersurfaces. See my Research Statement for more details.
Publications and Preprints
Accepted or published
- Xianzhe Dai and Junrong Yan. Witten Deformation for Noncompact Manifolds with Bounded Geometry, Journal of the Institute of Mathematics of Jussieu,38 pages
- Xianzhe Dai and Junrong Yan. Witten Deformation on Non-compact Manifold: Heat Kernel Expansion and Local Index Theorem, Math. Z., 31 pages
- Xinxing Tang and Junrong Yan. CY/LG correspondence for Weil-Petersson metrics and tt⁎ structures, Journal of Geometry and Physics, 34 pages
Preprints
- Junrong Yan. Witten Deformation for Non-Morse Functions and Gluing Formula for Analytic Torsions, ArXiv:2301.01990, 39 pages
- Junrong Yan. A New Analytic Proof of Gluing Formula for Analytic Torsion Forms, ArXiv:2301.02591, 38 pages
- Fagui Li and Junrong Yan. A First Eigenvalue Estimate for Embedded Hypersurfaces in Positive Ricci Curvature Manifolds, ArXiv:2308.02803, 10 pages
- Martin Puchol and Junrong Yan. Generalized Morse Functions, Excision and Higher Torsions, ArXiv:2407.17100, 107 pages
- Xianzhe Dai and Junrong Yan. Heat Kernel Approach to the Weyl Law for Schrödinger Operators on Non-compact Manifolds, ArXiv:2504.15551, 20 pages
- Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh and Junrong Yan. A Gluing Formula for the Z2-valued Index of Odd Symmetric Operators, Arxiv:2505.07094, 18 pages
In preparation
- Xianzhe Dai and Junrong Yan. Analytic Torsion for Witten Deformation on Non-compact Manifold
My Thesis
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Here are the projects that I am currently working on
Higher Cheeger-Mueller/Bismut-Zhang Theorem
This is a joint project with Martin Puchol and Yeping Zhang.
Gluing formula for Global invariants
Weyl’s law on metric geometry
This is a joint project with Xianzhe Dai.
BCOV torsion for LG models
This is in various parts joint with with Xianzhe Dai and Xinxing Tang.
Teaching
Instructor
- Math 3B: Calculus with Applications, Summer 2021
Teaching Assistant
- Math 8: Transitions to Higher Mathematics, Spring 2018
- Math 8: Transitions to Higher Mathematics, Fall 2018
- Math 6B: Vector Calculus, Winter 2019
- Math 34B: Calculus for Social and Life Sciences, Spring 2019
- Math 6A: Vector Calculus, Fall 2019
- Math 6A: Vector Calculus, Winter 2020
- Math 6A: Vector Calculus, Summer 2020
- Math 8: Transitions to Higher Mathematics, Fall 2020
- Math 6A: Vector Calculus, Winter 2021
- Math 6A: Vector Calculus, Spring 2021
Reader
- Math 117: Methods of Analysis, Fall 2017
- Math 108B: Introduction to Linear Algebra, Winter 2018
- Math 117: Methods of Analysis, Fall 2019
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