# Research

Research Interests (Keywords):

- Scaling limits of discrete random objects
- Discrete stochastic processes
- Random permutations, particularly pattern-avoiding permutations
- Bootstrap percolation and related growth models arising from statistical mechanics
- Asymptotic analysis of algorithms

## Papers (with links to arxiv preprints)

Papers (with links to arxiv preprints)

Published:

- Pattern-avoiding permutations and Brownian excursion, Part I: shapes and fluctuations (w/ Christopher Hoffman and Douglas Rizzolo in Random Structures and Algorithms, 2016)
- Pattern-avoiding permutations and Brownian excursion, Part II: fixed points (w/ Christopher Hoffman and Douglas Rizzolo in Probability Theory and Related Fields, 2016)
- Fixed points of 321-avoiding permutations (w/ Christopher Hoffman and Douglas Rizzolo in Proceedings of the American Mathematical Society, 2018)
- Local limit of the fixed point forest (w/ Tobias Johnson and Anne Schilling in Electronic Journal of Probability, 2017)
- The threshold for jigsaw percolation on random graphs (w/ Béla Bollobás, Oliver Riordan, and Paul Smith in Electronic Journal of Combinatorics, 2017)
- Neighborhood growth dynamics on the Hamming plane (w/ Janko Gravner and David Sivakoff in Electronic Journal of Combinatorics, 2017)
- Asymptotic distribution of fixed points of pattern-avoiding involutions (w/ Samuel Miner and Douglas Rizzolo in Discrete Mathematics & Theoretical Computer Science, 2017)
- The bullet problem with discrete speeds (w/ Brittany Dygert, Matthew Junge, Christoph Kinzel, Annie Raymond, and Jennifer Zhu in Electronic Communications in Probability, 2019)
- Maximal spanning time for neighborhood growth on the Hamming plane (w/ Janko Gravner and J.E. Paguyo in SIAM Journal on Discrete Mathematics, 2019)
- Expected size of a tree in the fixed point forest (w/ Samuel Regan in Discrete Mathematics & Theoretical Computer Science, 2019)

Submitted:

- Time scales of Fredricks0n-Andersen model on polluted Z
`2`

and Z3 (w/ Assaf Shapira) - Square permutations are typically rectangular (w/ Jacopo Borga)
- Bootstrap percolation on the Hamming torus with threshold 2
- Almost square permutations are typically square (w/ Jacopo Borga and Enrica Duchi)

In preparation:

- Pattern-avoiding permutations and Dyson Brownian Motion (w/ Christopher Hoffman and Douglas Rizzolo)

## Selected Talks

Selected Talks

Upcoming:

- JMM Special Session on Analytic and Probabilistic Combinatorics - Jan 16, 2020

Invited:

- Dartmouth Math Society (Undergraduate) - October 2019
- Dartmouth College Combinatorics Seminar - September 2019
- University of Warwick - May 2019
- Journeé Cartes at Paris XIII - April 2019
- Iowa State University Colloquium - March 2019
- CALIN University of Paris XIII Combinatorics Seminar - October 2018
- IRIF University of Paris VII Probability Seminar - November 2018
- Modal'X Probability Seminar - November 2019
- ICJ/UMPA Probability Seminar - November 2018
- American University of Paris (Undergraduate) - October 2018
- CUNY Probability Seminar - October 2018
- Duke University Probability Seminar - October 2018
- AMS Sectional Meeting Delaware - September 29-30th, 2018
- Howard Colloquium - September 2018
- George Washington University Combinatorics Seminar - September 27th, 2018
- International Vilnius Conference on Probability Theory, Lithuania - July 2018
- LPSM University of Paris VII - October 2017
- UC Davis probability seminar - February 2017
- Institut Henri Poincaré - January 2017
- USC Probability Seminar - March 2016
- Penn/Temple Probability Seminar - January 2016
- Dartmouth Colloquium - January 2016
- AMS Sectional Meetings Special Session on Discrete Stochastic Processes, Michigan State University - March 2015
- BAD Math Day, Stanford - September 2015

Contributed:

- Permutation Patterns, Dartmouth - July 2018
- Permutation patterns, Reykjavik University, - June 2017
- World Congress in Probability and Statistics, Toronto - July 2016
- Permutation Patterns, Howard University, - June 2016
- JCDCGG 2015, University of Kyoto - September 2015
- Lattice Path Combinatorics Conference, Cal State Polytechnic Pomona, - August 2015
- Stochastic Processes and Analysis, Oxford, - July 2015
- Permutation Patterns, London, - June 2015

### Conference Organizing:

Conference Organizing:

- Davis-Warwick Probability workshop- December 2015
- Bay Area Discrete Math Day- Fall 2016
- Permutation Patterns 2019

### Seminar Organizing:

Seminar Organizing:

- UC Davis Mathematical Physics and Probability Seminar- Spring 2015.