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.

### Math papers and preprints

• 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). Communications in Mathematical Physics (2021). [arXiv, doi]
• Tightness of Liouville first passage percolation for $$\gamma\in (0,2)$$ (with Jian Ding, Julien Dubédat, and Hugo Falconet). Publications Mathématiques de l'IHÉS 132 (2020), pp. 353–403. [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). Accepted at Archive for Rational Mechanics and Analysis. [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 Unpublished.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]

### Expository

Some mathematical visualizations (require a reasonably modern [in 2016] browser, e.g. Firefox or Chrome).

### Teaching

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."

### Contact

• Email: alexander DOT dunlap AT cims DOT nyu DOT edu.
• Office: WWH 1005B (but in practice for now online).
• ORCID
• Pronouns: he/him