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I am currently at the University of Pennsylvania as an Assistant Professor of Mathematics.
My research is in probability theory, with a focus on applying ideas from elliptic PDE to problems in statistical physics. I am interested in homogenization, which describes the large-scale behavior of random/periodic systems. I also study fluctuation-driven phenomena that emerge at small scales. Topics I have worked on include diffusions in random environments, Liouville quantum gravity, discrete unique continuation, and the Abelian sandpile. See this Quanta article for a non-technical discussion of some of my recent work.
Before coming to UPenn, I was an NSF Postdoctoral Fellow / Courant Instructor at the Courant Institute with Scott Armstrong. I spent the first year of my NSF postdoc at Cornell University with Lionel Levine. I received my PhD at the University of Chicago under the supervision of Charles K. Smart in June 2022. Previously, I was an undergraduate student at Stanford University.
I co-organize the Penn/Temple probability seminar.
Anthropic recently proved Kozma–Nitzan Conjecture 3, settling the long-standing conjecture that θ(pc) = 0 for Bernoulli bond percolation in every dimension. In roughly ten hours, ChatGPT Sol 5.6 Ultra produced complete proofs of the remaining Kozma–Nitzan conjectures, which Claude Fable 5.1 then formalized in Lean.
- Los Angeles Probability Forum, UCLA, December 3, 2026
- 47th Midwest Probability Colloquium, Northwestern University, October 15-17, 2026
- CUNY Probability Seminar, October 6, 2026
- Rutgers University Discrete Math Seminar, October 5, 2026
- AMS Fall Eastern Sectional Meeting, Special Session on Schramm–Loewner Evolutions (SLE) Theory and Random Matrix Theory (RMT), George Washington University, October 3-4, 2026
- AMS Fall Eastern Sectional Meeting, Special Session on the Geometry of Discrete Stochastic Spatial Models, George Washington University, October 3-4, 2026
- University of Bath Workshop, United Kingdom, September 7-11, 2026
- International Congress of Basic Science (ICBS), Invited Lecture, Beijing, August 10-21, 2026
- Coin Flippers 2026: The ICM Satellite Edition, University of Delaware, Newark, DE, July 21-22, 2026
- 45th Conference on Stochastic Processes and their Applications, Invited Session, Ithaca, June 14-20, 2026
- Statistical Mechanics of Lattice Systems (Maryland), March 2-6, 2026
- University of Maryland Probability Seminar, February 25, 2026
- Topological Phase Transitions and Localization of Random Fields (Chile), December 7-12, 2025
- CUNY Probability Seminar, October 28, 2025
- University of Wisconsin, PDE Geometric Analysis Seminar, October 27, 2025
- Columbia University, Probability Seminar, October 24, 2025
- ETH Zurich Analysis Seminar, March 18, 2025
- University of Toronto Mathematics Colloquium, January 15, 2025
- University of Southern California Mathematics Colloquium, January 13, 2025
- UCLA Mathematics Colloquium, January 8, 2025
- Vanderbilt Mathematics Colloquium, January 6, 2025
- University of South Carolina Mathematics Colloquium, December 10, 2024
- Duke Probability Seminar, December 5, 2024
- University of Pennsylvania Probability and Combinatorics Seminar, December 3, 2024
- University of Chicago Mathematics Colloquium, November 18, 2024
- University of Chicago Probability Seminar, October 4, 2024
- Yale Analysis Seminar, September 26, 2024
- IMSI, Two-Dimensional Random Geometry, July 8-12, 2024
- Aalto University, Probabilistic Field Theories, June 17-19, 2024
- MIT Analysis Seminar, April 16, 2024
- NYU Probability Seminar, April 12, 2024
- McGill University Probability Seminar, March 28, 2024
- The Fields Institute, KPZ meets KPZ, March 4-8, 2024
- Los Angeles Probability Forum, February 29, 2024
- University of Hagen, Analysis Seminar, November 29, 2023
- NYU Analysis Seminar, November 2, 2023
- AMS 2023 Fall Eastern Sectional Meeting, Special Session, September 9, 2023
- CIRM, Percolation and interactions, August 3, 2023
- 43rd Conference on Stochastic Processes and their Applications, Invited Session, July 26, 2023
- Percolation Today, April 4, 2023
- University of British Columbia Probability Seminar, March 1, 2023
- University of Victoria Dynamics and Probability Seminar, February 28, 2023
- Institute for Advanced Study Probability Seminar, November 2, 2022
- Penn/Temple Probability Seminar, November 1, 2022
- Cornell Probability Seminar, October 24, 2022
- Oberwolfach, Universality: Random Matrices, Random Geometry and SPDEs, June 4, 2022
- Yale Analysis Seminar, March 3, 2022
- University of Utah Stochastics Seminar, February 25, 2022
- LU-NU-UMN Joint Probability Seminar, October 27, 2021
- Bernoulli-IMS, Organized Session, July 22, 2021
- Stanford Probability Seminar, May 10, 2021
- UC Berkeley Probability Seminar, February 10, 2021
- Cornell Math 7710 Guest Lecture, October 27, 2020
- Cornell Probability Seminar, September 23, 2019
- CCNY Mathematics Colloquium, September 19, 2019
University of Pennsylvania
- In Spring 2026, I taught Math 6490 (the second semester of graduate probability).
New York University
- In Spring 2025, I taught MATH-UA 262 Ordinary Diff Equations.
- In Fall 2024, I taught MATH-UA 325 Analysis.
- In Fall 2023 and Spring 2024, I taught MATH-UA 120 Discrete Mathematics.
University of Chicago
- In Spring 2022 and 2019, I was a teaching assistant for STAT 383 Measure-Theoretic Probability 2.
- In Winter 2022, I was a teaching assistant for STAT 33910 Financial Statistics.
- In Fall 2021, I was a teaching assistant for STAT 312 Stochastic Processes.
- In Winter 2021, I was a teaching assistant for STAT 33910 Financial Statistics.
- In Spring 2020, I was a teaching assistant for STAT 234 Statistical Models and Methods.
- In Fall 2020, I was a teaching assistant for STAT 25150 Introduction to Mathematical Probability.
- In Fall 2017 and 2018, I was a teaching assistant for STAT 312 Stochastic Processes.
- In Winter and Spring 2017, I was a teaching assistant for STAT 220 Statistical Methods and Applications.
Chinese University of Hong Kong Shenzhen
- In Summer 2016, I was a lecturer for Introduction to Matrix Methods.
Stanford
- In Fall 2014 and 2015, I was a teaching assistant for Introduction to Matrix Methods.
- In Winter 2014, I was a teaching assistant for Convex Optimization.