Number Theory: Analytic, Combinatorial, Probabilistic.
Combinatorics: Additive and Probabilistic.
Probability Theory: Gaussian Multiplicative Chaos, Random Polynomials, Mixing time of Markov Chains.
Nonnegative quadratic character sums (With Rodrigo Angelo and K. Soundararajan)
[Annoucement at ICM 2022 by Soundararajan, video]
[Talk at Number Theory Webinar by myself, video]
In preparation
Distribution of random multiplicative functions in short intervals (With Adam J. Harper and K. Soundararajan)
In preparation
Crossing probabilities and random multiplicative functions (With R. Angelo, M. Aymone, J. Campos-Vargas, O. Klurman)
Submitted
Helson's conjecture for smooth numbers (With Seth Hardy)
Submitted
A random polynomial with multiplicative coefficients is almost surely irreducible (With Péter P. Varjú)
Submitted
Average sizes of mixed character sums (With Victor Y. Wang)
Submitted
Harper's beyond square-root conjecture (With Victor Y. Wang)
International Mathematics Research Notices 18 (2025), rnaf279
Better than square-root cancellation for random multiplicative functions
Transactions of the American Mathematical Society. Series B 11 (2024), 482–507
Extreme values of Dirichlet polynomials with multiplicative coefficients (with Daodao Yang)
Journal of Number Theory 258 (2024), 173-180
Central limit theorems for random multiplicative functions (with Kannan Soundararajan)
[Video, Sound]
[Video, myself]
Journal d'Analyse Mathématique, 2023 (special volume to celebrate Peter Sarnak's 70th birthday)
Paucity phenomena for polynomial products (with Victor Y. Wang)
Bulletin of the London Mathematical Society, 2024
Partial sums of typical multiplicative functions over short moving intervals (with Mayank Pandey and Victor Y. Wang)
Algebra & Number Theory, 18(2):389–408, 2024
On a Turán conjecture and random multiplicative functions (with Rodrigo Angelo)
[Video]
Quarterly journal of mathematics, 74 (2023), 767-777
On the random Chowla conjecture
(with Oleksiy Klurman and Ilya D. Shkredov)
Geometric and Functional Analysis, 33 (2023), 749–777.
Universality of low degree factors of random polynomials over finite fields
(with Jimmy He and Huy Tuan Pham)
International Mathematics Research Notices, 2023 (17), 14752-14794
On product sets of arithmetic progressions (with Yunkun Zhou)
[Video]
Discrete Analysis 2023:10, 31 pp.
Discrepancy of arithmetic progressions in grids (with Jacob Fox and Yunkun Zhou)
Mathematika, 70 (2024), no. 1, Paper No. e12237, 31 pp.
Discrepancy in modular arithmetic progressions (with Jacob Fox and Yunkun Zhou)
[Video]
Compositio Mathematica 158 (2022), 2082-2108.
Multicolor list Ramsey numbers grow exponentially (with Jacob Fox, Xiaoyu He, and Sammy Luo)
Journal of Graph Theory, 101 (2022), 389–396.
Mixing time of fractional random walk on finite fields (with Jimmy He and Huy Tuan Pham)
[Video, talk by Jimmy He]
Electronic Journal of Probability, 27 (2022), 1-15
A note on the Erdős distinct subset sums problem (with Quentin Dubroff and Jacob Fox)
SIAM Journal on Discrete Math. 35 (2021), 322-324.
A polynomial with a root mod p for all p has a real root (with Rodrigo Angelo)
The American Mathematical Monthly, accepted.
Irreducibility of random polynomials of bounded degree (with Huy Tuan Pham)
[Editorial introduction]
Discrete Analysis 2021:7, 16 pp.
A robust version of Freiman's 3k-4 Theorem and applications (with Fernando Xuancheng Shao)
Mathematical Proceedings of the Cambridge Philosophical Society 166 (2019), 567-581.
Popular differences and generalized Sidon Sets
Journal of Number Theory 186 (2018), 103-120
Arithmetic properties of random polynomials (Supervisor: Prof. Péter Varjú )