I work on probabilistic number theory and stochastic partial differential equations (SPDEs).
In probabilistic number theory, I mainly focus on establishing limiting distribution of certain number-theoretic functions, e.g., prime divisor counting function, the Riemann zeta function, Dirichlet L-functions, etc. Also, I am interested in "importing" number theory techniques into theory of probability.
In SPDEs, in addition to the well-posedness of equations, I am also interested the probabilistic properties of solutions, e.g., does the solution admit a stationary distribution? How fast does the system converge to its stationary distribution? Does the system admit a large deviation estimate?
Aside from mathematics, I am fond of philosophy of science, especially HPS, the sociology of scientific knowledge (SSK), and the history of madness.
I have collaborated with Hao-Lun Fu (傅皓倫), James T. Townsend, and Cheng-Ta Yang (楊政達) in a project regarding face cognition, which directly relates to the study of artificial intelligence.
On rates of convergence in central limit theorems of Selberg and Bourgade (with Peng-Jei Wong). [arXiv]
Log-correlation for shifted Dirichlet 𝐿-functions and Dedekind zeta functions of quadratic fields (with Peng-Jei Wong). Forum Math., vol. 38, no. 2, 2026, pp. 339-360. https://doi.org/10.1515/forum-2023-0224
Three-dimensional stochastic Navier-Stokes equations with Markov switching (with P. Sundar). Stoch. Dyn. 23 (2023), no.7, Paper No. 2350057, 41 pp. [arXiv] [SD]
Ergodicity for three-dimensional stochastic Navier-Stokes equations with Markovian switching (with P. Sundar). Stoch. Anal. Appl.42 (2024), no.1, 264–287. [arXiv] [SAA]
On Selberg's central limit theorem for Dirichlet L-functions (with Peng-Jie Wong). Journal de Théorie des Nombres de Bordeaux 32 (2020), 685-710. [PDF] [JTNB]
Exponential inequalities for exit times for stochastic Navier-Stokes equations and a class of evolutions (with P. Sundar). Communications on Stochastic Analysis 12 (2018), 343-358. [PDF ] [COSA]
On the Varying Density of Faces in Face Space: Explanation of the Atypicality Effect in Terms of a Riemannian Metric and Potential Application to the Other Race Effect (with Cheng-Ta Yang , Hao-Lun Fu , Cheng-Ju Hsieh , and James T. Townsend), submitted, [preprint].
