Analysis Student Seminar Fall 2021
The Analysis Student Seminar meets on Mondays at 4:00 PM. In the Fall semester of 2021 the topic is “Random walks, harmonic functions, and boundaries at infinity”
Current Schedule
| Date | Speaker | Topic | Source |
|---|---|---|---|
| Aug. 25 | Yankl Mazor | Organization; general overview | Various |
| Aug. 30 | Yankl Mazor | Introduction to random walks on groups; | Chapter 1 of Lalley’s notes |
| Sept. 6 | Labor Day | - | - |
| Sept. 13 | Yankl Mazor | Subadditive limits and random walks | Lalley, Chapter 2 |
| Sept. 20 | Owen Mireles Briones | The Carne-Varopoulos Inequality | Lalley, Chpater 3 |
| Sept. 27 | Paul Sweeney | Amenability and return probabilities | Lalley, Chapter 4 |
| Oct. 4 | Yankl Mazor | Harmonic functions on groups and random walks pt 1 | Lalley, Chapter 5 |
| Oct. 18 | Yankl Mazor | Harmonic functions on groups and random walks pt 2 | Lalley, Chapter 5 |
| Oct. 25 | Willie Lim | Entropy and harmonic functions | Lalley, Chapter 6 |
Sources:
The primary source to start with will be these notes from Steve Lalley on random walks on infinite groups
A primer on probability from Greg Lawler: (https://www.math.uchicago.edu/~lawler/probnotes.pdf)
Other possible sources
Harmonic measures versus quasiconformal measures for hyperbolic groups, S. Blachere, P. Haissinsky, and P. Matthieu (2009)
Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry, M. Duchin (2005)
The Poisson formula for groups with hyperbolic properties, V. Kaimanovich (1998)
Amenability via random walks, L. Bartholdi and B. Virag (2003)
See also:
Video sources
Poisson-Furstenberg boundaries and the kaimanovich-vershik conjecture, by Russell Lyons
The Poisson boundary: a qualitative theory, by Vadim Kaimanovich - Lecutres 1, 2, 3, 4