Chongyao Chen

I am a fifth-year PhD student in mathematics at Duke University. I am interested in algebraic geometry and mathematical physics. My advisor is Colleen Robles and my co-advisor is Kirsten Wickelgren. I'm on the job market this Fall 2024.

Before starting my PhD at Duke, I obtained a PhD in Theoretical Physics from Peking University, where I studied the phenomenology of particle physics. Before that, I obtained a BSc in Mathematics and concurrently a BA in History from Peking University.

Email: chongyao.chen at duke dot edu

Research

My main research interests are Hodge theory, enumerative geometry, and D-modules. From time to time, I am also enjoy using mathematics to solve practical problems. Here is a list of my publications and preprints. Google Scholar homepage

Algebraic geometry

Quadratically enriched binomial coefficients over a finite field, with K. Wickelgren. arXiv:2412.14277
On the generic degree of two-parameter period mappings, with H. Deng. arXiv:2408.12090
Extension of a 2D period image of Hodge type (1,2,2,1). Accepted by Advances in Theoretical and Mathematical Physics, arXiv:2311.10212
Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of P[r], with S. Guo. Acta Mathematica Sinica, English Series 40 (1), 43-80. URL link

Applied mathematics and physics

Improve Representation for Imbalanced Regression through Geometric Constraints, with Z. Dong, Y. Wu, Y. Zou, Y. Zhang, J. Zhou. Accepted by CVPR 2025, arXiv.2503.00876
Representation Theorem for Multivariable Totally Symmetric Functions, with Z. Chen and J. Lu. Communications in Mathematical Sciences, Vol. 22, No. 5 (2024), pp. 1195-1201. URL link
Mixup your own pairs, with Y. Wu, Z. Dong, W. Zhou, J. Zhou. arXiv:2309.16633
Quantum numbers of the pentaquark states via symmetry analysis, with M. Chen and Y. Liu. Communications in Theoretical Physics 72 (12), 125202. URL Link
A modification of Faddeev–Popov approach free from Gribov ambiguity, with F. Gao and Y. Liu. Communications in Theoretical Physics 72 (12), 125201. URL Link
Colour Confinement: a Dynamical Phenomenon of QCD, with F. Gao, Y. Liu. arXiv:1802.08184.

Conferences and workshops attended

Derived Categories and Mirror Symmetry, Madison, May 28 - June 1, 2025
IAS/PCMI 2024 Graduate Summer School: Motivic Homotopy Theory, Park City, July 8-26, 2024
Singularities in Ann Arbor, Ann Arbor, May 13-17, 2024. Poster presented
Concluding Conference of Simons Collaboration on Homological Mirror Symmetry, Stony Brook, April 25-28, 2023
Periods, Shafarevich Maps and Applications, Miami, Jan 30-Feb 3, 2023
Mathematical physics: algebraic cycles, strings and amplitudes, Cambridge, UK, July 19-22, 2022

Teaching

Math 590 Algebraic D-modules (Instructor of record), Spring 2024
- Course description: This is an introductory course on algebraic D-modules. In this course, we will cover the basic properties of D-modules with emphasis on the regular holonomic D-modules. Then we will study different operations on D-modules and prove some important theorems including the Riemann-Hilbert correspondence and the Kashiwara equivalence. We will end with some applications of D-modules on toric geometry, i.e. the GKZ hypergeometric system.
Math 112L Laboratory Calculus II (TA), Spring 2023
Math 218D-1 Introduction to Linear Algebra (Discussion leader), Fall 2022
Math 620 Smooth Manifolds (Grader), Fall 2021
Math 111L Laboratory Calculus I (Discussion leader), Fall 2021

Outreach

Research Experiences for Undergraduates (REU): Enriched binomial coefficients (TA), Summer 2024
Math+ program: Moduli of weighted hyperplane arrangements and degenerations (TA), Summer 2023