Schedule

April 17 - Pauwel Van Den Eeckhaut (Bonn)

Title: Local rigidity of self-joinings and factors of pro-nilsystems

Abstract:

Pro-nilsystems play a central role in ergodic structure theory: they are precisely the structured systems governing multiple ergodic averages. In this talk I will discuss a fundamental property of this class of dynamical systems, namely its stability under taking factors. More precisely, I will explain a direct proof that any factor of an ergodic $k$-step pro-nilsystem is again a $k$-step pro-nilsystem. The main new ingredient is a local rigidity result for ergodic self-joinings of nilsystems: any ergodic self-joining sufficiently close to the diagonal joining is in fact the graph joining of an automorphism. The key geometric input here is a ‘no small subnilmanifolds’ lemma. I will then sketch how this rigidity result can be used to prove the factor-closure of pro-nilsystems.

April 24 - Alexander Volberg (MSU and Bonn)

Title: The Boolean surface area of polynomial threshold functions

Abstract: Link to Abstract

Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and isoperimetric properties of the class, especially bounds on average sensitivity, one of the central themes in the study of PTFs since the Gotsman–Linial conjecture.

In this work we exhibit a new geometric sense in which PTFs are tightly constrained, by studying them through the lens of the Boolean surface area (or Talagrand boundary):

$\textbf{BSA} [f] = \textbf{E} |∇ f | = \textbf{E} \sqrt{Sens_f (x)},$

which is a natural measure of vertex-boundary complexity on the discrete cube. Our main result is that every degree-d PTF $f$ has subpolynomial Boolean surface area:

$\textbf{BSA} [f] ≤ exp(C(d) \sqrt{log n}).$

This is a superpolynomial improvement over the previous bound of $n^{1/4} (log n)^{C(d)}$ that follows from Kane’s landmark bounds on average sensitivity of PTFs [?].

Degree-$d$ PTFs thus satisfy a stronger form of geometric regularity than was previously visible from influence bounds alone. As an application, we obtain improved noise sensitivity estimates in the case of small noise parameter.

May 1 - No Seminar

May 8 - Davi Castro-Silva (University of Cambridge)

Title: An algorithmic Polynomial Freiman-Ruzsa theorem

Abstract:

In a major advance in additive combinatorics, Gowers, Green, Manners, and Tao resolved the long-standing Polynomial Freiman-Ruzsa (PFR) conjecture, which characterizes approximate subgroups with only polynomial loss in parameters. This result bridges combinatorial and algebraic notions of structure, and has wide-ranging implications across combinatorics and theoretical computer science.

In this talk, I will introduce the context of the PFR theorem and describe recent joint work with Jop Briët, Srinivasan Arunachalam, Arkopal Dutt, and Tom Gur, in which we develop efficient algorithms for several equivalent formulations of this theorem. A key feature of our work is the development of new bridges connecting additive combinatorics with symplectic geometry and quantum computation.

Based on the preprint arXiv:2604.04547.

May 15 - Stefanos Lappas (Bonn)

Title: Sharp bilinear estimates for singular integral operators and their maximal counterparts with kernels in weighted spaces

Abstract:

We discuss the boundedness properties of bilinear singular integral operators (including their maximal versions) associated with rough homogeneous kernels on $R$. In particular, we focus on the $L^{p_1} (R) \times L^{p_2} (R) \to L^p (R)$ bounds in the optimal quasi-Banach range of exponents $1 < p_1 , p_2 < \infty$ and $1/2 < p < \infty$, when the angular component $\Omega$ of the kernel belongs to weighted $L^q$-spaces on the unit sphere $S^1$ and has vanishing integral. This talk is based on two joint works with Petr Honzík, Lenka Slavíková and Bae Jun Park.

May 22 - Elias Schuster (Bonn)

Title: TBA

Abstract:

TBA

May 29 - No Seminar

June 5 - Bonn-Cologne Analysis & PDE Workshop 2026

Location: Lipschitz Lecture Hall

Schedule and Abstract:

Our group member Robert Schippa will give a talk in this event.

June 12 - Jesse Reimann (TU Delft)

Title: Schur multipliers of divided differences and their boundedness

Abstract:

TBA

June 19 - Double Session

Talk 1 - 14:15 - Sebastián Muñoz (Paris)

Title: TBA

Abstract:

TBA

Talk 2 - 15:15 - Ying Wang (Basque Center for Applied Mathematics)

Title: TBA

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TBA

June 26 - Joseph Adams (Heinrich-Heine-Universität Düsseldorf)

Title: TBA

Abstract:

TBA

July 3 - Double Session

Talk 1 - 14:15 - Ethan Ackelsberg (EPFL)

Title: TBA

Abstract:

TBA

Talk 2 - 15:15 - Tatjana Eisner (University of Leipzig)

Title: TBA

Abstract:

TBA

July 10 - Double Session

Talk 1 - 14:15 - Joris Roos (University of Massachusetts Lowell)

Title: TBA

Abstract:

TBA

Talk 2 - 15:15 - Polona Durcik (Chapman University)

Title: TBA

Abstract:

TBA

July 17 - Luka Milicevic (Serbian Academy of Sciences and Arts)

Title: TBA

Abstract:

TBA

July 24 - Lenka Slavikova (Charles University)

Title: TBA

Abstract:

TBA