To connect people working in topics around dynamical systems in Scotland.
The University of Glasgow (Contacts: Jim Belk, Vaibhav Gadre, Xin Li, and Mike Whittaker)
Heriot-Watt University (Contacts: Matthew Cordes and Alessandro Sisto)
University of St Andrews (Contacts: Natalia Jurga, Mike Todd and Stephen Cantrell)
Date: Friday 19th September 2025
Location: University of St Andrews (icebreaker meeting)
11-12.30 (St Andrews)
11-11.30 Mike Todd
11.30-11.45 Steve Cantrell
11.45-12 Saeed Shaabanian
12-12.30 Natalia Jurga
12.30-1.30 lunch
1.30-3 (Glasgow)
1.30-2 Mike Whittaker
2-2.15 Philipp Bader
2.15-2.30 Ujan Chakraborty
2.30-3 Xin Li
3-3.30 coffee
3.30-4.45 (Heriot Watt)
3.30-4 Matt Cordes
4-4.15 Giorgio Mangioni
4.15-4.45 Alex Sisto
5pm onwards: pub and dinner
Local organisers: Natalia Jurga and Mike Todd
Speaker: Ujan Chakraborty
Title: Ergodic Operator Inequalities for Unimodular Amenable Groups through Random Walks
Abstract: Existing proofs of pointwise ergodic theorems for amenable groups are quite involved. This is principally due to the difficulty in obtaining the maximal inequality. Assuming unimodularity, we provide a new and transparent proof of these theorems using random walks that deals with the classical and noncommutative cases on an equal footing. We show that one may dominate the average on the group by that on the integers (a Markov operator). Maximal inequalities and pointwise convergence follow as corollaries.
Speaker: Giorgio Mangioni
Title: Random quotients preserve non-positive curvature
Abstract: A random walk on a finitely generated group G is an infinite sequence of group elements, each of which differs from the previous by a random generator. One can then define a random quotient by modding out the n-th steps of a collection of independent random walks, and study the behaviour of such quotient as the step n goes to infinity. In this talk we illustrate how several notions of "non-positive curvature" for groups survive under random quotients. As a case study, we show that random quotients of hyperbolic groups are again hyperbolic, providing a new proof of a theorem of Delzant (1996). This is joint work with Carolyn Abbott, Daniel Berlyne, Thomas Ng, and Alex Rasmussen.
