Higher Cheeger–Müller / Bismut–Zhang theorem
Higher torsion, generalized Morse functions, and excision. Joint with Martin Puchol and Yeping Zhang.
Zelevinsky Postdoctoral Fellow · Northeastern University
Junrong
Yan
My research lies at the interface of analysis, geometry, topology, and mathematical physics. A central question guiding my work is: how can techniques from global analysis and index theory be used to understand spectral problems and to construct and compare geometric and topological invariants?
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About
About me.
I am a Zelevinsky Postdoctoral Fellow at Northeastern University, working with Maxim Braverman.
I received my Ph.D. from the University of California, Santa Barbara in 2022 under the supervision of Xianzhe Dai. Before joining Northeastern, I was a Boya Postdoctoral Fellow at BICMR, Peking University, working with Xiaobo Liu. I began my studies at Nankai University.
Outside mathematics, I enjoy Yu-Gi-Oh!, cycling, and swimming.
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Current projects
Current
directions
My work sits at the intersection of global analysis on manifolds, quantum field theory, and partial differential equations—with a focus on spectral invariants, Landau–Ginzburg models, and holomorphic field theories.
Gluing formulas for global invariants
Analytic and topological gluing phenomena for spectral invariants and torsion forms.
Weyl laws on metric geometry
Spectral asymptotics for Schrödinger operators on noncompact spaces. Joint with Xianzhe Dai and Maxim Braverman.
BCOV torsion for LG models
Geometry and topology of Landau–Ginzburg B-models, in parts with Xianzhe Dai and Xinxing Tang.
Feynman graph integrals
Renormalization and holomorphic field theories on Kähler manifolds. Joint with Minghao Wang.
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Research
Publications
& preprints
Published, accepted, and current manuscripts.
Published & accepted 05
[1] Witten Deformation for Non-Morse Functions and Gluing Formula for Analytic Torsions
To appear in Communications in Analysis and Geometry
[2] A First Eigenvalue Estimate for Embedded Hypersurfaces in Positive Ricci Curvature Manifolds ↗
Differential Geometry and its Applications
[3] CY/LG Correspondence for Weil–Petersson Metrics and tt* Structures ↗
Journal of Geometry and Physics
[4] Witten Deformation for Noncompact Manifolds with Bounded Geometry ↗
Journal of the Institute of Mathematics of Jussieu
[5] Witten Deformation on Non-compact Manifold: Heat Kernel Expansion and Local Index Theorem ↗
Mathematische Zeitschrift
Preprints 07
[10] Feynman Graph Integrals on Kähler Manifolds ↗
arXiv:2507.09170
[13] Generalized Morse Functions, Excision and Higher Torsions ↗
arXiv:2407.17100
In preparation
Xianzhe Dai · Junrong Yan. Analytic Torsion for Witten Deformation on Non-compact Manifolds.
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Teaching
In the
classroom
I value clear motivation, structural understanding, and the freedom to experiment with ideas.
Instructor of record
MATH 7371 · Morse Theory
Northeastern University
MATH 2331 · Linear Algebra
Northeastern University
MATH 1342 · Calculus 2 for Science & Engineering
Northeastern University
MATH 1342 · Calculus 2 for Science & Engineering
Northeastern University
Calculus 2
Peking University
MATH 3B · Calculus with Applications
UC Santa Barbara
Undergraduate mentoring
Jiasheng Lin · Morse theory and Floer homology
Kai Yan & Xinzhe Li · Gauge theory, TQFT, and knot theory
Teaching assistant & reader experience +
Teaching assistant for ten courses at UC Santa Barbara (2018–2021), including Transitions to Higher Mathematics, Vector Calculus, and Calculus for Social and Life Sciences. Reader for Methods of Analysis and Introduction to Linear Algebra.