I am an NSF postdoc at NYU Courant, sponsored by Jean-Christophe Mourrat. I study problems in probability theory, partial differential equations, and applied math. I got my Ph.D. from Stanford in 2020, advised by Lenya Ryzhik.

- A forward-backward SDE from the 2D nonlinear stochastic heat equation (with Yu Gu). Submitted. [arXiv]
- Viscous shock solutions to the stochastic Burgers equation (with Lenya Ryzhik). Submitted. [arXiv]
- The continuum parabolic Anderson model with a half-Laplacian and periodic noise. Electronic Communications in Probability
**25**(2020), paper no. 64. [arXiv, doi] - Existence of stationary stochastic Burgers evolutions on \(\mathbf{R}^2\) and \(\mathbf{R}^3\). Nonlinearity
**33**(2020), no. 12, pp. 6480–6501. [arXiv, doi] - Stationary solutions to the stochastic Burgers equation on the line. (with Cole Graham and Lenya Ryzhik). Submitted. [arXiv]
- Tightness of Liouville first passage percolation for \(\gamma\in (0,2)\) (with Jian Ding, Julien Dubédat, and Hugo Falconet). Publications Mathématiques de l'IHÉS (2020). [arXiv, doi]
- Subsequential scaling limits for Liouville graph distance
(with Jian Ding). Communications in Mathematical Physics
**376**(2020), pp. 1499–1572. [arXiv, doi] - Fluctuations of the solutions to the KPZ equation in dimensions three and higher
(with Yu Gu, Lenya Ryzhik, and Ofer Zeitouni). Probability Theory and Related Fields
**176**(2020), no. 3–4, pp. 1217–1258. [arXiv, doi] - Constructing a solution of the \((2+1)\)-dimensional KPZ equation
(with Sourav Chatterjee). Annals of Probability
**48**(2020), no. 2, pp. 1014–1055. [arXiv, doi]. - The random heat equation in dimensions three and higher: the homogenization viewpoint (with Yu Gu, Lenya Ryzhik, and Ofer Zeitouni). Submitted. [arXiv].
- Liouville first-passage percolation: subsequential scaling limit at high temperature
(with Jian Ding). Annals of Probability
**47**(2019), no. 2, pp. 690–742. [arXiv, doi] - Expected regularized total variation of Brownian motion. Unpublished. [arXiv]

Some mathematical visualizations (require a reasonably modern browser, e.g. an updated version of Chrome or Firefox):

I am not teaching in 2020–21.

Teaching at Stanford:

- 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)."

Teaching at Chicago:

- Spring 2014: TA for Math 28410 "Honors Combinatorics."
- 2012–2013: Junior Tutor (section leader) for Math 13100–13200–13300 "Elementary Functions and Calculus."

- Email: alexander DOT dunlap AT cims DOT nyu DOT edu.
- Office: WWH 1005B (but in practice for now online).
- ORCID