Leonid Petrov - Integrable Probability

About • (papers) • (CV)

Professor of Mathematics, University of Virginia.

Leonid Petrov works in integrable probability, an area of mathematical research at the interface between probability / statistical physics on the one hand and representation theory/quantum integrability on the other. He applies tools from integrability (symmetric functions and Yang-Baxter equations for solvable lattice models) to analyze the asymptotic behavior of stochastic models motivated by a wide range of real-world questions, including the structure of ice and other condensed matter, magnetism, quantum spin systems, thermodynamics, traffic models, and directed polymers.

Petrov completed his Ph.D. in 2010 in Moscow with advisor Grigori Olshanski. Following a postdoctoral position at Northeastern University (2011-2014), he joined the University of Virginia as faculty in Department of Mathematics. He has held visiting positions at MIT (2017-2018), MSRI (Fall 2021), and IPAM (Spring 2024).

Recently, he is also involved in broadening access to AI tools for working mathematicians by sharing best practices, participating in panel discussions, and utilizing AI to build interactive simulations of cutting-edge research advances in integrable probability and beyond (see below for a few comprehensive examples).

Keywords: Integrable probability, KPZ universality, interacting particle systems, six vertex model, Yang-Baxter equation, stochastic vertex models, Bethe ansatz, Macdonald processes, random tilings, symmetric functions, algebraic combinatorics

• NSF grant 2153869 "Random Systems from Symmetric Functions and Vertex Models" (2022-2025).
• Focused Research Group in Integrable Probability (opens in new tab) (2017-2022) supported by the NSF grant 1664617 (opens in new tab) and companion grants 1664531 (opens in new tab), 1664619 (opens in new tab), 1664650 (opens in new tab).

Teaching • (all)

In Spring 2026, I teach an Engagements course "Building Truth from Scratch" (from Jan 12 to March 9).
Syllabus • (PDF for printing). Class meets: Mon/Wed 5:00-6:15pm.
Office Hours: Tue 10-11am, Thu 10-11am, or by appointment (make appointments by email).

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Recent news and links

• Math Experimental Lab: Random Surfaces and Random Permutations — Spring 2026 project page.
• Blue Ridge Probability Day, March 13, 2026 at University of Virginia.
• If you're using BibTeX and alpha bibliography style or amsrefs, but don't like the ordering of same-author references, process your .bbl file through this bibliography sorting tool before submitting to arXiv.
• Reflections on teaching math with AI (slides, June 2025)
• I organized a workshop "All roads to the KPZ universality class" at American Institute of Mathematics (Pasadena, CA) from March 17 to 21, 2025. This page contains useful resources for participants.
• Simulations of random permutations from the staircase reduced word, based on the paper [45].
• Slides for the talk "How we can use AI in Math work" (October 2024 at UVA)

Students and postdocs

• Yizhen Li, Ph.D. student 2024-29
• Mikhail Tikhonov, Ph.D. student 2020-26 (postdoc at Oregon State University starting Fall 2026)
• Daniel Slonim, postdoc 2022-24 (now Tenure Track at Hillsdale College)
• Svetlana Gavrilova, bachelor thesis at HSE, 2020-21 (now Ph.D. student at MIT)
• Milind Hegde, postdoc at MSRI Fall 2021 (now Tenure Track at NTU Singapore)
• Axel Saenz, postdoc 2016-19 (now Tenure Track at Oregon State)