I am primarily interested in probability and combinatorics. My research is currently focused on percolation 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.
- Critical Percolation and the Incipient Infinite Cluster on Galton-Watson Trees
- Quenched Survival of Bernoulli Percolation on Galton-Watson Trees joint with Robin Pemantle and Josh Rosenberg
- Central limit theorems from the roots of probability generating functions joint with Julian Sahasrabudhe
- Invasion Percolation on Galton-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)