Plenary talks

28.07.2025, 9:00 (Monday morning)

Title: Mobile sampling on the sphere

Abstract: Mobile sampling is a form of data acquisition where a multivariate function is sampled by a single sensor along a continuous curve. We study mobile sampling on the sphere for spaces of polynomials of given degree. The question is when and how a polynomial can be recovered from its values along a curve on the sphere. This problem can be approached either by proving sampling inequalities (in this context often called Marcinkiewicz-Zygmund (MZ) inequalities) or by means of quadrature rules. Whereas for pointwise sampling the cost is usually measured by the number of samples, in mobile sampling the cost is measured by the length of the curve. Necessary conditions for MZ inequalities imply a lower bound for the length of a curve. We present a construction of MZ-curves by means of geodesic cycles that matches the correct length. Here a geodesic cycle is a closed curve that connects finitely many points along great circles. The construction of curves satisfying a quadrature rule is more difficult and is connected to the theory of spherical t-designs. For the sphere we explain a construction of $t$-design curves with asymptotically optimal length, for higher-dimensional spheres we can show the existence of $t$-design curves.

28.07.2025, 14:20 (Monday afternoon)

Title: Linear algebraic perspectives on modern broadband signal processing

Abstract: In this talk, we present a linear algebraic framework for addressing a number of challenges in modern broadband signal processing. We will explore the fundamental role of the Slepian basis, which offers an optimal representation for finite-length windows of bandlimited signals. A key focus will be on how recent theoretical breakthroughs have enabled the development of novel computational tools and allowed us to overcome historical computational bottlenecks, transforming these theoretically powerful tools into practically viable solutions in large-scale problem settings.

Building upon this foundation, we will describe a number of applications of these ideas to problems in array processing, such as broadband beamforming and source localization, treating these as linear inverse problems. We will demonstrate how this approach leads to significantly improved estimation performance, surpassing traditional filter-based methods, and enabling substantial power savings through reduced array readout. We will also show that through a straightforward extension, this high performance can be maintained even with significant uncertainty in the angle of arrival, demonstrating the inherent robustness of this framework. These results highlight how adopting a linear algebraic perspective can provide simple, yet powerful, solutions to the complex challenges inherent in modern roadband signal processing.

29.07.2025, 9:00 (Tuesday morning)

Title: Inference in High Dimensions, Algorithms, and Random Matrices

Abstract: In this talk I plan to both give an introduction to non-asymptotic (and potentially inhomogeneous) random matrix theory, including recent results; and to illustrate how non-asymptotic random matrix theory is a crucial tool in understanding both the performance of efficient algorithms in solving high dimensional statistical inference tasks, as well as fundamental obstacles to do so.

29.07.2025, 14:20 (Tuesday afternoon)

Title: Sampling determinantal point processes on a quantum computer

Abstract: Be it feature selection in regression or graph sparsification, many data science applications can be formulated as selecting a small representative subset of a larger ground set of N items. Determinantal point processes (DPPs) are probability distributions originating in quantum optics, which allow selecting such representative subsets at a reasonable computational cost, and sometimes yield better-than-iid statistical guarantees. I will show that, given access to a quantum computer with as many qubits as the cardinality N of the ground set (an unrealistic assumption in 2025), one can sample a large class of determinantal point processes faster than on a classical computer. The talk is based on Reference [2]. I will try to stick to a level of exposition that does not require any prior affinity with quantum computing, but if you have time prior to the talk, you can read Section 3 of [1] for a 3-page introduction to some of the notions I’ll use.

This talk is based on joint work with Michaël Fanuel and Alexandre Feller.

[1] https://arxiv.org/abs/2305.15851

[2] https://arxiv.org/abs/2503.05906

30.07.2025, 9:00 (Wednesday morning)

Title: Dimension reduction properties and supervised learning of complex Functional Data

Abstract: Abstract: Functional data, originating from random variables valued in a functional space, present significant challenges when it comes to modeling curves, patterns, images, and other intricate structures. This talk focuses on dimension reduction methods (PCA) crafted specifically for complex functional datasets. We will give an overview of functional data, emphasizing their frequent presence in domains like geostatistical, environmental fields and biomedical research. A key emphasis will be placed on the theoretical aspects of Functional Principal Component Analysis of spatial and non-random samples. We’ll explore some practical implementations aimed at capturing variability, dimensionality reduction and supervised learning.

30.07.2025, 14:20 (Wednesday afternoon)

Title: From Generative AI to Statistical Physics Through Sparse Harmonic Analysis

Abstract: Score based diffusions generate impressive models of images, sounds and complex physical systems. Are they generalising or memorising ? How can deep network estimate high-dimensional scores without curse of dimensionality ? This talk shows that generalisation does occur for deep network estimation of scores, with enough training data. We prove that these deep networks perform a denoising by shrinking image coefficients in a best basis adapted to the image geometry. The ability to avoid the curse of dimensionality seems to rely on multiscale properties revealed by a renormalisation group decomposition coming from statistical physics. Applications to models of physical turbulent flows will be introduced and discussed.

31.07.2025, 9:00 (Thursday morning)

Title: The Intersection between Compressed Sensing and Error Correction

Abstract: Compressed sensing and error correction share deep structural connections, but also exhibit important differences. Over the past two decades, these connections have enabled the transfer of ideas, techniques, and guarantees between them. For instance, combinatorial objects such as block designs and difference sets allow constructions of deterministic measurement matrices in compressed sensing and structured codes in error correction. In 2016, new results in coding theory showed that symmetry alone is sufficient for structured codes to achieve capacity on erasure channels, with Reed-Muller codes emerging as the key example. Subsequent work for general memoryless symmetric channels has so far shown that symmetry, while an essential element, must be coupled with additional structural properties to establish capacity-achieving performance. For compressed sensing, this is more complicated because the notion of capacity is typically replaced by predictions of the reconstruction error based on the replica method from statistical physics. In parallel, advances in compressed sensing have improved our understanding of deterministic measurement matrices—particularly equiangular tight frames—and their performance under random erasures. In this talk, we review the history of these connections with a focus on recent advances. Then, we conclude with a discussion of interesting open problems—highlighting both key technical barriers and compelling conceptual challenges.

01.08.2025

Title: TBA

Abstract: TBA