**Time:** 2:00 PM, August 16th, 2022. **Place: **Laurent Schwartz Hall, VIASM

The public lecture will be organized by VIASM in partnership with Clay Mathematics Institute - CMI (https://www.claymath.org/), a part of the VIASM - ICTP Summer School in Group Theory and Representation Theory, organized by VIASM in coordination with ICTP.

**Title**: Probabilistic group theory and its applications

**Content:**

It is a well-known and elementary fact that any finite symmetric group *S**n *can be generated by two of its elements – for example, by a 2-cycle and an *n*-cycle. Much less elementary is the fact, proved by John Dixon in 1969 (and conjectured by Eugen Netto in 1892), that if *p**n *denotes the probability that two randomly chosen permutations generate either *S**n *or its alternating subgroup *A**n*, then *p**n **→ *1 as *n → ∞*. Dixon conjectured that similar results should hold for other families of finite simple, or nearly simple, groups such as the special linear groups *SL*(*n, *F*q*), and the sudy of this and related questions led to the birth of a whole new field of probabilistic group theory. This field has turned out to have many connections and applications to other areas – for example, to the study of random walks on finite groups; to the analysis of algorithms in computational algebra; to the theory of representation varieties of various geometrically defined classes of infinite groups; and to decidability questions for finitely presented groups.

In the lecture I will attempt to give the flavour of this new field of probabilistic group theory, and also to present some of its applications.

**Lecturer:**

**Dr. Martin Liebeck** (Imperial College London)

Dr. Liebeck is one of the leading scientists in group theory and has published over 150 articles and books on finite and algebraic groups, representation theory, probabilistic group theory, and applications of these topics to areas such as model theory in logic, Markov theory in probability, combinatorics, and the design of algorithms in computational algebra.

Dr. Liebeck is a Fellow of the American Mathematical Society and was the recipient of the London Mathematical Society’s Polya Prize in 2020..

**Registration:**

There is no registration needed. The lecture is open to the public.

Contact: viasm-ictp-ss2022@viasm.edu.vn