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)

• Bootstrap percolation on the Hamming torus with threshold 2

• 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:

• Davis-Warwick Probability workshop- December 2015

• Bay Area Discrete Math Day- Fall 2016

• Permutation Patterns 2019

Seminar Organizing:

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