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 hierarchical Pitman-Yor processes (with Stefano Favaro & Shui Feng)
Publications & Preprints:
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)
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
Central limit theorem for crossings in randomly embedded graphs (with Santiago Arenas-Velilla & Octavio Arizmendi) (2023), 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)
Convergence rates of limit theorems in random chord diagrams (2021), perpetual preprint
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: The 1st Annual Meeting of the West Coast Coin Flippers Union
August 2024, [slides]
Central limit theorem 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]
Sampling unlabeled structures via the Burnside process
USC Combinatorics Seminar
October 2022, [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]
Discrete interacting particle systems
USC Graduate Student Colloquium
October 2021 [slides, video]
Maximal spanning time for neighborhood growth on the Hamming plane
USC Graduate Student Algebra Seminar
October 2019