Dynamic afternoon at Warwick

Dynamic afternoon at Warwick

When: 27.10.2025, 13:00-18:00

Where: D1.07 Zeeman Building, Univ. Warwick

Schedule:

11:45-13:00: Lunch at Nexus Café - former NAIC café (meet at 11:45 in the common room)

13:00-13:55: Joel Moreira (Warwick, Coventry):

Finding infinite patterns in sets with positive density

14:00-14:55: Han Yu (Warwick, Coventry)

Multiplicative approximation on manifolds: the convergence theory

15:00-16:00: Coffee pause at the common room

16:05-17:00: Michal Rams (IMPAN, Warsaw)

Smoothness of random self-similar measures on the line

17:05-18:00: Richard Aoun (Univ. Gustave Eiffel, Paris)

Random walks on projective spaces : stationary measures and topological recurrence

18:00 - 18:45: Walk/bus to the restaurant (to be determined)

18:45 - : Dinner

List of speakers: Richard Aoun, Joel Moreira, Michal Rams, Han Yu.

Titles & Abstracts:

Richard Aoun

Title: Random walks on projective spaces : stationary measures and topological recurrence

Abstract: In this talk, we survey recent results on discrete time Markov chains on projective spaces induced by i.i.d random walks on the general linear groups. We investigate their topological recurrence in some specific models including the well-known affine recursions, through the existence of stationary Radon measures. Based on recents works with C. Sert and with S. Brofferio and M. Peigné.

Joel Moreira

Title: Finding infinite patterns in sets with positive density
Abstract: Old questions in additive combinatorics and Ramsey theory ask what infinite patterns are unavoidable in sets of natural numbers with positive density, but until recently, there were no positive answers. In the last few years a new technique was developed to address such questions, making use of ergodic theory and dynamical systems, which were previously restricted to handling finite patterns. In this talk I will briefly survey the history of the subject, explain the connection to ergodic theory, and describe how we used this technique to answer a question of Paul Erdos regarding infinite sumsets. The talk will be based on joint work with Bryna Kra, Florian Richter and Donald Robertson.

Michal Rams

Title: Smoothness of random self-similar measures on the line

Abstract: Consider the simplest case of random self-similar measures: let $\{f_i\}_{i=1}^k$ be an affine iterated function system on the line, with similarity dimension larger than 1. Let $p=(p_i)_{i=1}^k$ be a probabilistic vector, and we will consider the $p$-Bernoulli measure (which we will also assume has its similarity dimension greater than 1). Let us add randomness in the form of random translation perturbation of every map (independent perturbation on every node of the symbolic tree). We will assume the perturbations are nice, for example they might have absolutely continuous distribution with smooth density. Then the result of Jordan, Pollicott, Simon states that almost every realization of this random limit set has positive Lebesgue measure and the random Bernoulli measure is almost surely absolutely continuous with $L^2$ density. Lately, Dekking, Simon, Sz\'ekely, Szekeres proved that almost surely the random limit set contains an interval, and Gu, Miao have described the $L^q$ dimenion.

What we prove is as follows: under the above assumptions we can prove that the density of random Bernoulli measure is almost surely H\"older continuous. It is a joint work with Bal\'azs B\'ar\'any.

Han Yu

Title: Multiplicative approximation on manifolds: the convergence theory

Abstract: A classical result of Gallagher (1962) tells us how Lebesgue measures process zero-full laws, capturing how a typical vector is approximated by rationals. A major problem in the field of metric diophantine approximation is to extend those results to surface carried measures on manifolds, leaving the results for Lebesgue measure as special cases. In this context, the convergence theory, which holds trivially for Lebesgue measures via the Borel-Cantelli lemma, turns out to be very challenging. In this talk, we shall illustrate the convergence Gallagher theory for non-degenerate or flat manifolds following some Fourier analytic ideas, sampling from earlier works (Huang (2024), Technau-Srivastava (2024), Chow-Yu (2024)).

This is a joint work (in progress) with Sam Chow (Warwick), Rajula Srivastava (Wisconsin–Madison), and Nichlas Technau (Wisconsin–Madison).

Organizers

Tom Rush - Cagri Sert