About me        Research        Teaching        

About me.

I started my undergraduate study in 2013 at School of Mathematical Science, Nankai University, Tianjin, China.

I obtained 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

j.yan@northeastern.edu

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 research interests are in geometric analysis, QFT, and PDE. In particular, I am currently studying the geometry and topology of Landau-Ginzburg B-model, holomorphic field theories, gluing formulas for global spectral invariants, and the comparison geometry of hypersurfaces. For more details, please see my Research Statement.

Publications and Preprints

Accepted or published

1. Xianzhe Dai and Junrong Yan. Witten Deformation for Noncompact Manifolds with Bounded Geometry, Journal of the Institute of Mathematics of Jussieu，38 pages
2. Xianzhe Dai and Junrong Yan. Witten Deformation on Non-compact Manifold: Heat Kernel Expansion and Local Index Theorem, Math. Z., 31 pages
3. Xinxing Tang and Junrong Yan. CY/LG correspondence for Weil-Petersson metrics and tt^⁎ structures, Journal of Geometry and Physics, 34 pages

Preprints

1. Junrong Yan. Witten Deformation for Non-Morse Functions and Gluing Formula for Analytic Torsions, ArXiv:2301.01990, 39 pages
2. Junrong Yan. A New Analytic Proof of Gluing Formula for Analytic Torsion Forms, ArXiv:2301.02591, 38 pages
3. Fagui Li and Junrong Yan. A First Eigenvalue Estimate for Embedded Hypersurfaces in Positive Ricci Curvature Manifolds, ArXiv:2308.02803, 10 pages
4. Martin Puchol and Junrong Yan. Generalized Morse Functions, Excision and Higher Torsions, ArXiv:2407.17100, 107 pages
5. Xianzhe Dai and Junrong Yan. Weyl Law for Schrödinger Operators on Noncompact Manifolds, Heat Kernel, and Karamata-Hardy-Littlewood Theorem, ArXiv:2504.15551, 20 pages
6. 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
7. Minghao Wang and Junrong Yan. Feynman Graph Integrals on Kähler Manifolds, ArXiv:2507.09170, 49 pages

In preparation

1. 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 and Maxim Braverman.

BCOV torsion for LG models

This is in various parts joint with with Xianzhe Dai and Xinxing Tang.

Feynman graph integral

This is a joint project with Minghao Wang

Teaching

Instructor

1. Math 3B: Calculus with Applications, Summer 2021

Teaching Assistant

1. Math 8: Transitions to Higher Mathematics, Spring 2018
2. Math 8: Transitions to Higher Mathematics, Fall 2018
3. Math 6B: Vector Calculus, Winter 2019
4. Math 34B: Calculus for Social and Life Sciences, Spring 2019
5. Math 6A: Vector Calculus, Fall 2019
6. Math 6A: Vector Calculus, Winter 2020
7. Math 6A: Vector Calculus, Summer 2020
8. Math 8: Transitions to Higher Mathematics, Fall 2020
9. Math 6A: Vector Calculus, Winter 2021
10. Math 6A: Vector Calculus, Spring 2021

Reader

1. Math 117: Methods of Analysis, Fall 2017
2. Math 108B: Introduction to Linear Algebra, Winter 2018
3. Math 117: Methods of Analysis, Fall 2019

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