My research interests are in discrete probability, combinatorial stochastic processes, Markov chains, Stein's method, & Bayesian nonparametrics. Here is my CV.
I am currently thinking about:
Pattern occurrences in random pattern-avoiding permutations (with Erik Slivken)
Asymptotic behavior of the hierarchical Pitman-Yor process (with Shui Feng)
Chinese restaurant process down-up Markov chains (with Noah Forman)
Publications & Preprints:
Central limit theorem for crossings in randomly embedded graphs (with Santiago Arenas-Velilla & Octavio Arizmendi), to appear in Journal of Theoretical Probability
Cycle structure of random parking functions, Advances in Applied Mathematics, 144 (2023), 102458
Maximal spanning time for neighborhood growth on the Hamming plane (with Janko Gravner & Erik Slivken), SIAM Journal on Discrete Mathematics, 33 (2) (2019), 976-993
Limit distributions for cycles in random parking functions (with Mei Yin) (2025), submitted
Asymptotic behavior of clusters in hierarchical species sampling models (with Stefano Favaro & Shui Feng) (2025), submitted
Central limit theorems associated with the hierarchical Dirichlet process (with Shui Feng) (2024), submitted
Mixing times of a Burnside process Markov chain on set partitions (2022), submitted
Fixed points, descents, and inversions in parabolic double cosets of the symmetric group (2021)
Limit theorems for three random discrete structures via Stein's method, PhD thesis, University of Southern California, (2023)
Slow neighborhood growth on the Hamming plane, Undergraduate honors thesis, University of California Davis, (2017)
Invited Talks:
Species sampling problems and the Dirichlet process, Cal Poly Pomona Mathematics Colloquium, February 2025, [slides]
Homozygosity of the hierarchical Dirichlet process, McMaster Statistics Seminar, September 2024, [slides]
Homozygosity of the hierarchical Dirichlet process, Coin Flippers 2024, August 2024, [slides]
CLT for crossings in randomly embedded graphs, The Ohio State University Combinatorics and Probability Seminar, February 2024, [slides]
Crossings, random graphs, and Stein's method, McMaster University Mathematics Colloquium, January 2024, [slides]
The mathematics of card shuffling, McMaster Casual Math Seminar, November 2023, [slides]
Sampling unlabeled structures via the Burnside process, McMaster Statistics Seminar, November 2023, [slides]
Mixing times of a Burnside process on set partitions, AMS Fall Eastern Sectional Meeting, SUNY Buffalo, September 2023, [slides]
Convergence rates of limit theorems in random chord diagrams, University of Denver Analysis Seminar, April 2023, [slides]
Convergence rates of limit theorems in random chord diagrams, Dartmouth Combinatorics Seminar, April 2023, [slides]
Limit theorems in parabolic double cosets of the symmetric group, Graduate Student Combinatorics Conference, March 2023, [slides]
Cycle structure of random parking functions, Permutation Patterns 2022 , June 2022, [slides]
Limit theorems in parabolic double cosets of the symmetric group, Southern California Discrete Mathematics Symposium, May 2022, [slides]
Cycle structure of random parking functions, USC Probability Seminar, April 2022, [slides, video]