Research

Research interest

My research lies in probability theory and its applications to complex systems arising from nature and societies. It includes not only the design and analysis of stochastic models to develop a rigorous understanding of the system under study, but also the integration of observed data into solving challenging problems. I am particularly interested in cancer evolution, virus infection spread, hurricane dynamics, and other spatial stochastic systems in population genomics, ecology, and earth and atmospheric sciences. My inclusive approach fosters perspectives and collaborations across disciplines. See my Research Statement for more details. 

Selected publications organized roughly by research areas:

Stochastic modeling and analysis

1. Stochastic PDEs on graphs as scaling limits of discrete interacting systems. Bernoulli. 27(3), 899-1941, 2021.

2. Wave propagation for reaction-diffusion equations on infinite trees. With W. Hu and G. Terlov. Communications in Mathematical Physics. 384, 2021.

3. Systems of interacting diffusions with partial annihilations through membranes. With Z.-Q. Chen. Annals of Probability. Vol.45, 100-146, 2017.

Population genetics and genomics

4. Bursts of coalescence within population pedigrees whenever big families occur. With D. Diamantidis, M. Birkner and J. Wakeley. Genetics, 2024. (Featured article in the May 2024 issue).

5. Recurrent mutation in the ancestry of a rare variant. With J. Wakeley*, E. Koch and S. Sunyaev. Genetics. Vol 224 (3), 2023  (*Joint first author).

6. Genealogies in expanding populations. With R. Durrett. Annals of Applied Probability. Vol. 26 (6), 3456-3490, 2016.

Mathematical biology 

7. Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles. With Q. Liang, Y. J. Yang, W.-C. Lo. PLOS Computational Biology, 19(10), 2023.

8. Constrained Langevin approximation for the  Togashi-Kaneko model of autocatalytic reactions. With Y. J. Yang and C. Yuan. Mathematical Biosciences and Engineering (special issue in stochastic methods for biological systems). Vol20 (3), 2023. 

9. Ellipsoidal Brownian self-driven particles in a magnetic field. With On Shun Pak and Mario Sandoval. Physical Review E, 95 (3), 032605, 2017.

Phylogenetics 

10. An impossibility result for phylogeny reconstruction from k-mer counts. With B. Legried and S. Roch. Annals of Applied Probability. 32(6), 2022.

11. Statistically consistent and computationally efficient inference of ancestral DNA sequences in the TKF91 model under dense taxon sampling. With S. Roch. Bulletin of Mathematical Biology. Vol 82 (2), 2020.

12. Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees. With S. Roch. Electronic Journal of Probability, Vol. 23 (47), 1-24, 2018.

Earth and atmospheric sciences 

13. Three-dimensional shear driven turbulence with noise at the boundary. With M. Jolly and A. Pakzad. Nonlinearlity. Vol 34 (7), 2021.

14. Hitting time of rapid intensification onset in hurricane-like vortices. With C. Kieu, D. Sakellariou and M. Patra. Physics of Fluids, 33(9) 2021. 

15. Stochastic Variability of Tropical Cyclone Intensity at the Maximum Potential Intensity Equilibrium. With Phuong Nguyen and Chanh Kieu. Journal of the Atmospheric Sciences. 77 (9), 3105-3118, 2020.

Slides and Posters

1. Indiana Research Experience for Undergraduate (REU) Keynote Lecture 2023 

2. Wave propagation for reaction-diffusion equations on random trees.

3. Identification and estimation for Markov processes on phylogenetic trees.

4. Stochastic spatial models for complex systems.