# 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