Laplacian growth: Sandpiles, rotor routers and their scaling limits
Organizers
Speaker
Time
Monday, March 9, 2026 2:35 PM - 3:15 PM
Venue
A6-101
Online
Zoom 388 528 9728
(BIMSA)
Abstract
The Abelian sandpile was discovered more than thirty years ago, independently in Statistical Physics, Algebra and Combinatorics. It has strong connections to Potential Theory. The related rotor-router model offers an alternative approach to fair division of indivisible particles. We survey the progress made on describing scaling limits of these models on Euclidean lattices as the mesh size goes to zero, starting with the circularity result for internal DLA by Lawler-Bramson-Griffeath. These models yield attractive simulations and many intriguing open problems. (Lecture based on forthcoming book with Ahmed Bou-Rabee and Lionel Levine)
Speaker Intro
Yuval Peres obtained his PhD in 1990 from the Hebrew University, Jerusalem. He was a postdoctoral fellow at Stanford and Yale, and was then a Professor of Mathematics and Statistics in Jerusalem and in Berkeley. Later, he was a Principal researcher at Microsoft. In 2023, he joined Beijing Institute of Mathematical Sciences and Applications. He has published more than 350 papers in most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has co-authored books on Markov chains, probability on graphs, game theory and Brownian motion, which can be found at https://www.yuval-peres-books.com. His presentations are available at https://yuval-peres-presentations.com. He is a recipient of the Rollo Davidson prize and the Loeve prize. He has mentored 21 PhD students including Elchanan Mossel (MIT, AMS fellow), Jian Ding (PKU, ICCM gold medal and Rollo Davidson prize), Balint Virag and Gabor Pete (Rollo Davidson prize). He was an invited speaker at the 2002 International Congress of Mathematicians in Beijing, at the 2008 European congress of Math, and at the 2017 Math Congress of the Americas. In 2016, he was elected to the US National Academy of Science.