Professor Jérémie Brieussel (University of Montpellier, Geometric Group Theory) will deliver the Mathematics and Mathematical Sciences Global Special Lecture 1 as follows.
If you wish to attend, please register using the Google form below.

◆Date and Time:
April 13 (Mon) – April 17 (Fri), 2026
13:00–15:00 each day

◆Venue:
Room 127, Building No. 3, Graduate School of Science

Title:
Random walks on infinite groups

Abstract：
A random walk is the sequence of products of independent elements of
a group following a given probability law. A finitely generated group can be
viewed as a geometric object by means of its Cayley graph, thus a random
walk is a way to explore randomly the geometry of a group. What properties
of the group are reflected in the random walk ? It turns out, and this is the
aim of this course, that there are various connexions between characteristics
of the random walk and algebraic, geometric, analytic and dynamical features
of the group.

- Lecture 1: Kesten’s theorem relating return probability to the Cheeger
constant of isoperimetry.
- Lecture 2: Tail events and harmonic functions, entropy criterion for Liouville
property.
- Lecture 3: Poisson boundary, ray criterion for identification.
- Lecture 4: Choquet-Deny groups are virtually nilpotent.
- Lecture 5: A panoramic view of finitely generated groups through the eyes
of a random walker.
The course is aimed to be self-contained and will assume no specific prior
knowledge.

Registration:
Those who wish to attend are required to register via the Google Form.
Please access the form using the QR code or the URL below:

https://forms.gle/P2WfZYnVshXnmxMY7

Registration Deadline
April 6 (Monday)

✧✧Notes✧✧

Mathematics and Mathematical Sciences Global Lecture IV is a core course of the Mathematics and Mathematical Sciences Innovation Human Resource Development Program.

To receive course credit, registration through KULASIS is required.
(Course registration period for first-semester courses: April 17 (Fri) – April 20 (Mon))

Auditing is permitted even without KULASIS registration (limited to Kyoto University students).
Registration via the Google Form is still required.

For further details, including abstracts of each special lecture, please visit the program website:
https://www.math.kyoto-u.ac.jp/ja/ktgu/courses