# 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)

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)

Square permutations are typically rectangular (w/ Jacopo Borga in Annals of Applied Probability [accepted] 2020)

Submitted:

Time scales of Fredricks0n-Andersen model on polluted Z2 and Z3 (w/ Assaf Shapira, 2019)

Almost square permutations are typically square (w/ Jacopo Borga and Enrica Duchi, 2021)

Preprint:

Scaling limits of permutations avoiding long decreasing sequences (w/ Christopher Hoffman and Douglas Rizzolo 2020)

## Selected Talks

Invited:

Amherst - January 2020

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

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:

### Seminar Organizing:

UC Davis Mathematical Physics and Probability Seminar- Spring 2015.