I'm broadly interested in the theory and applications of probability and stochastic processes. I have been working on research projects on random polynomials, random graphs, Markov Chains, and the phase transition of the contact process. I'm eager to explore new research directions and their applications.
Current funding: National Science Foundation DMS - 2125031
Random functions and universality of the distribution of roots
- Random orthonormal polynomials: universality and expected number of real roots (with Yen Do and Van Vu), arXiv preprint arXiv:2012.10850, 2020. [pdf][abs]
- Random trigonometric polynomials: universality and non-universality of the variance for the number of real roots (with Yen Do and Hoi Nguyen), to appear in Annales de l’Institut Henri Poincaré - Probabilités et Statistiques. [pdf][abs]
- Random polynomials: central limit theorems for the real roots (with Van Vu), to appear in Duke Math Journal. [pdf][abs]
- Roots of random functions: a framework for local universality (with Van Vu), to appear in the American Journal of Mathematics. [pdf][abs]
- Random eigenfunctions on flat tori: universality for the number of intersections (with Mei-Chu Chang, Hoi Nguyen and Van Vu), International Mathematics Research Notices, 2020(24), 2020, 9933-9973. [pdf]
- Roots of random polynomials with coefficients of polynomial growth (with Yen Do and Van Vu), The Annals of Probability 46(05), 2018, 2407–2494. [pdf]
- On the number of real roots of random polynomials (with Hoi Nguyen and Van Vu), Communications in Contemporary Mathematics 18(04), 2016, 1550052. [pdf]
Stochastic processes: contact process, mixing time of Markov chains
- On the spectrum of random walks on complete finite d-ary trees (with Evita Nestoridi), Electronic Journal of Probability 26, 2021, 1-17. [pdf]
- Critical value asymptotics for the contact process on random graphs (with Danny Nam and Allan Sly), to appear in the Transactions of the American Mathematical Society. [pdf][abs]
- Survival and extinction of epidemics on random graphs with general degrees (with Shankar Bhamidi, Danny Nam and Allan Sly), The Annals of Probability 49(01), 2021, 244-286. [pdf]
- On the mixing time of the Diaconis-Gangolli random walk on contingency tables over Z/qZ (with Evita Nestoridi), Annales de l’Institut Henri Poincaré - Probabilités et Statistiques 56(2), 2020, 983–1001. [pdf]
Combinatorial problems on random graphs
- Embedding large graphs into a random graph (with Asaf Ferber and Kyle Luh), Bulletin of the London Mathematical Society 49(05), 2017, 784–797. [pdf]
- Packing loose Hamilton cycles (with Asaf Ferber, Kyle Luh and Daniel Montealegre), Combinatorics, Probability and Computing 26(06), 2017, 839-849. [pdf]
Anti-concentration inequalities
- Anti-concentration for polynomials of independent random variables and applications in complexity theory (with Raghu Meka and Van Vu), Theory of Computing 12(11), 2016, 1-17. [pdf]
