Alan Zhao
4th Year Ph.D. Candidate
Affiliation: Columbia University
Co-advised by Ivan Corwin and Dorian Goldfeld
Email: asz2115 "at" columbia "dot" edu
Research Interests
I work on problems in number theory and integrable probability that invite the use of analytic and combinatorial techniques. For example, when I do number theory, I enjoy thinking about the Kuznetsov trace formula, Poisson summation formula, and counting problems in relative trace formulae; in probability, I am currently thinking about Gibbsian line ensembles, the geometric RSK correspondence, and the Yang-Baxter equation.
Research
- Oscillations in the Kuznetsov Trace Formula (preprint available upon request)
- J. Getz, A. Gutiérrez Terradillos, F. Hosseinijafari, B. Hu, S. Lee, A. Slipper, M. Tomé, H. Yao, A. Zhao, Modulation groups (submitted)
- J. Getz, A. Gutiérrez Terradillos, F. Hosseinijafari, A. Slipper, G. Xi, H. Yao, A. Zhao, The ρ-Fourier transform (submitted)
- A. Zhao, Heights of Rational Points on Mordell Curves (Journal of Number Theory)
Seminars
- Fall 2026: Analytic Number Theory and the Orbit Method
- Spring 2026: The Orbit Method and Subconvexity II
- Fall 2025: The Orbit Method and Subconvexity I
- Spring 2025, Fall 2024: Learning Seminar on Automorphic Forms
- Spring 2024: Sieves in Number Theory
Other Writing
- On a Kuznetsov Formula Without Continuous Spectrum (classical approach to "Oscillations in the Kuznetsov Trace Formula")