Online (ETA=) Ergodic Theory & Analysis Seminar
This is an online seminar in ergodic theory and analysis understood in a broad sense and their applications in additive combinatorics and additive number theory. The ETA seminar is aimed at a general mathematical audience. Graduate and postdoctoral students are especially welcome. Please subscribe here to attend.
Time: Wednesday, 11:00 a.m. Eastern Time (New York).
Location: Zoom. Please subscribe here to receive email notifications and the Zoom link for upcoming ETA seminar talks.
Contact: etaseminar[at]gmail.com
Organizers: Leonidas Daskalakis, Bartosz Langowski, Mariusz Mirek, Jakub Niksiński and Tomasz Z. Szarek.
Schedule: Spring 2026
Abstract: High-dimensional phenomena constitute a research theme that has been present in harmonic analysis for several decades. It was initiated by E. M. Stein in the 1980s and important contributions were made by J. Bourgain, A. Carbery and D. Müller. The study of dimension-free estimates for Hardy-Littlewood maximal functions in the discrete setting was initiated several years ago by J. Bourgain, E. M. Stein, M. Mirek and myself. One of the most important open problems in this field is a question of E. M. Stein about dimension-free estimates for discrete maximal function over Euclidean balls. During my talk I will report on recent progress on this question. Namely, in joint work with J. Niksiński, we gave an affirmative answer to Stein’s question when the supremum is restricted to small enough radii. An important part of our argument is a uniform (dimension-free) count of lattice points in high-dimensional spheres and balls with small radii. We also established a dimension-free estimate for a multi-parameter maximal function of a combinatorial nature, which is a new phenomenon and may be useful for studying similar problems in the future.
Abstract: An equation is partition regular over its domain if, for any finite coloring of that domain, there exists a monochromatic nontrivial solution. In this talk, we will review the background of this topic, focusing on the ergodic theoretic tools used to tackle such problems and present a recent joint work with A. Koutsogiannis, A. Ferré Moragues and W. Sun, concerning the partition regularity problem of quadratic equations over some number fields.
Abstract: See the attached file
Abstract: Favard length of a planar set is the average length of its orthogonal projections. The Besicovitch projection theorem, which is one of the cornerstones of geometric measure theory, states the following: if a set E of finite length has positive Favard length, then there exists a rectifiable curve intersecting E in a set of positive length. In this talk I will discuss my recent quantification of this classical result, and its application to Vitushkin’s conjecture.
Abstract: I will discuss recent developments concerning the distribution of rational points on the unit sphere, with connections to the covering radius problem and some number-theoretic problems.
Abstract: In this talk, I will discuss a new method of systematically treating a family of problems extending the Falconer distance problem, which asks for the optimal dimensional threshold so that any set larger than that must generate a distance set of positive Lebesgue measure. Our method produces nontrivial dimensional thresholds for the analogs of this problem with distance replaced by any finite graphs, and the threshold is surprisingly strong for several key examples such as cycles. In addition, we obtain results that allow for the graphs to be pinned at multiple places, further strengthening the conclusions even in some classical settings such as chains. This is joint work with Tainara Borges, Ben Foster, Eyvi Palsson, and Francisco Romero Acosta.
Abstract: See the attached file
Abstract: TBA.