I am primarily interested in probability and combinatorics. My research is currently focused on percolation on Galton-Watson trees as well as the distribution of coefficients of polynomials based on the location of their roots. My advisor is Robin Pemantle.
I took my qualifying exam on November 10, 2015; I had a major topic of probabilistic combinatorics and a minor topic of algebraic number theory.
- Invasion Percolation on Galton-Watson Trees joint with Robin Pemantle and Josh Rosenberg
- Three Central Limit Theorems Based on the Locations of Roots of Probability Generating Functions joint with Julian Sahasrabudhe
- Quenched Survival of Bernoulli Percolation on Gatlon-Watson Trees joint with Robin Pemantle and Josh Rosenberg
- Invasion Percolation on Galton-Watson Trees (October 2017)
- The Cap Set Problem and Ellenberg and Gijswijt's Recent Results (June 2016)
- Random Matrices and the Semicircle Law (February 2018)
- Branching Processes: Random Trees and Percolation on Them (October 2017)
- Random Graphs and Their Zero One Laws (February 2017)
- Simple Random Walks and Electrical Networks (September 2016)
- Probabilistic Methods in Ramsey Theory (January 2016)
- An Exposition of the Catalan Numbers (September 2015)
- Introduction to Quantum Computing (October 2014)