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 and participating in panel discussions. He also serves as an AI guide for Department of Mathematics, University of Virginia.

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 (2017-2022) supported by the NSF grant 1664617 and companion grants 1664531, 1664619, 1664650.

Teaching • (all)

In Spring 2025, I teach Random Matrices, a graduate topics course. All details are on the course webpage.

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Recent news and links

Students and postdocs

• Mikhail Tikhonov, Ph.D. student 2020-26
• 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)
• Axel Saenz, postdoc 2016-19 (now Tenure Track at Oregon State)