Alex Dunlap's home page
I'm a fifth-year Ph.D. student in the Mathematics Department of Stanford University, advised by Lenya Ryzhik. I am interested in probability, PDE theory, and applied math. In particular, I have been studying aspects of stochastic partial differential equations and Liouville quantum gravity. Before coming to Stanford I did my undergraduate work at the University of Chicago. I am grateful for the support of the National Science Foundation through a Graduate Research Fellowship.
Papers and preprints
(with Jian Ding, Julien Dubédat, and Hugo Falconet) Tightness of Liouville first passage percolation for \(\gamma\in (0,2)\). Submitted.
(with Jian Ding) Subsequential scaling limits for Liouville graph distance. Submitted.
(with Yu Gu, Lenya Ryzhik, and Ofer Zeitouni) Fluctuations of the solutions to the KPZ equation in dimensions three and higher. Accepted at Probability Theory and Related Fields.
(with Sourav Chatterjee) Constructing a solution of the (2+1)-dimensional KPZ equation. Accepted at Annals of Probability.
(with Yu Gu, Lenya Ryzhik, and Ofer Zeitouni) The random heat equation in dimensions three and higher: the homogenization viewpoint. Submitted.
(with Jian Ding) Liouville first-passage percolation: subsequential scaling limit at high temperature. Annals of Probability, Volume 47, Number 2 (2019), 690-742.
Expected regularized total variation of Brownian motion. Unpublished.
Some mathematical visualizations (require a reasonably modern browser, e.g. an updated version of Chrome or Firefox):
- Fall 2019: TA for Math 61CM "Modern Mathematics: Continuous Methods" (honors linear algebra and advanced calculus).
- Spring 2019: TA for Math 63CM "Modern Mathematics: Continuous Methods" (honors ordinary differential equations).
- Winter 2019: CA for Math 104 "Applied Matrix Theory."
- Summer 2018, Winter 2018, Summer 2017: CA for the real analysis part of Math 382 "Qualifying Examination Seminar."
- Fall 2017: TA for Math 61CM "Modern Mathematics: Continuous Methods" (honors linear algebra and advanced calculus).
- Winter 2017: CA for Math 205B "Real Analysis" (graduate course).
- Fall 2016: TA for Math 41 "Calculus (Accelerated)."
- Spring 2014: TA for Math 28410 "Honors Combinatorics."
- 2012–2013: Junior Tutor (section leader) for Math 13100–13200–13300 "Elementary Functions and Calculus."
- Email: apply the permutation (1 5 2 4 3) to the list of words "edu DOT ajdunl2 stanford AT".
- Address: Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, CA 94305.
- Office: 380-J.
- on GitHub.
- Unlike a former Stanford student whose name is the same as mine, I am extremely bad at baseball.
Places I've been or visited