遍历论 / Ergodic Theory
Ergodic theory is the study of measure-preserving transformations. These arise in several areas of mathematics, for example, in probability, number theory, information theory, and geometry. From its beginnings in Poincaré's recurrence theorem in celestial mechanics and Boltzmann's ergodic hypothesis in statistical physics, ergodic theory has had several waves of advances, in the 1930s, in the 1970s and 80s, and since the turn of the century. This course will introduce measure-preserving transformations (with many examples), prove some important general theorems, and in broad strokes introduce the main accomplishments of each wave. Time permitting, we will also highlight some modern applications of the theory in additive combinatorics and number theory.
On Fridays, there is no lecture, and the TA will run office hours for students at Tsinghua University.
On Fridays, there is no lecture, and the TA will run office hours for students at Tsinghua University.
Lecturers
Date
20th February ~ 5th June, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 09:50 - 12:15 | Online | ZOOM 13 | 637 734 0280 | BIMSA |
| Friday | 16:10 - 16:55 | Online | ZOOM 14 | 712 322 9571 | BIMSA |
Video Public
Yes
Notes Public
No
Lecturer Intro
Andrew Best attained his PhD in 2021 from the Ohio State University under the supervision of Vitaly Bergelson, was a postdoc at BIMSA starting from 2021, and became an assistant professor at BIMSA in 2024. He works on ergodic theory and its interactions with number theory and additive combinatorics.
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.
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.