Conférenciers

Programme

Conférenciers pléniers

Conférence Israel Gohberg ILAS-IWOTA

La conférence Israel Gohberg ILAS-IWOTA a été introduite en août 2016 et rend hommage à l'héritage d'Israël Gohberg, dont les recherches ont franchi les frontières entre la théorie des opérateurs, l'algèbre linéaire et des domaines connexes. Cette conférence est en collaboration avec l'International Linear Algebra Society (ILAS). Les dons pour le Fonds de conférences Israel Gohberg ILAS-IWOTA proviennent de particuliers et d'entreprises. Plus particulièrement, Springer/Birkhäuser Verlag soutient l'IWOTA depuis 1983 avec ses actes dans la série Operator Theory: Advances and Applications (OTAA). Springer/Birkhäuser Verlag est également un contributeur majeur au Fonds de conférences Israel Gohberg ILAS-IWOTA. Les dons sont toujours les bienvenus via le site ILAS : ilasic.org.

Résumé des conférences

Emmanuel Fricain, Dynamical properties of Toeplitz operators

In this talk, I will review some recent results concerning the hypercyclicity of Toeplitz operators on the Hardy space. An operator T is said to be hypercyclic if there exists a vector x whose orbit under T is dense. Motivated by results of Shkarin and Abakoumov–Baranov–Charpentier–Lishanskii, we investigate the case of Toeplitz operators with smooth symbols. Using a beautiful model developed by Yakubovich and the Godefroy–Shapiro criterion, we obtain, in some cases, a complete characterization. This is a joint work with S. Grivaux and M. Ostermann.

Pamela Gorkin, Finding Ellipses: The connection between Blaschke products and the numerical range

The numerical range of an $n \times n$ complex matrix A is defined by

\[W(A) = \{<Ax, x> : x \in C^n , \|x\|= 1\}.\]

In general, it’s not easy to compute the shape of the numerical range. In this talk, we investigate the question of when numerical ranges of matrices are elliptical by connecting this phenomenon to two seemingly different settings: function theory and projective geometry. Starting with $n = 2$ and extending to general $n$ leads to a class of operators known as compressions of the shift operator. This viewpoint provides new insight into the numerical ranges of these operators and highlights special features that emerge when the numerical range is an ellipse.

Lajos Molnár, Isometries and maps preserving means on positive cones in operator algebras

Building on the extensive study of linear isometries on algebras of functions, matrices, and operators (see, e.g., the Banach–Stone theorem and its extension for $C^*$-algebras given by Kadison), we consider nonlinear isometries of positive cones in operator algebras with respect to some distinguished metrics. These mappings turn out to be closely related to transformations that are algebraic morphisms with respect to certain operator means as binary operations. In the talk, we will present an overview of our results concerning these types of geometric and algebraic transformations.

Akram Aldroubi, Operator Iterations, Frames, and Dynamical Sampling

Dynamical sampling is a framework encompassing a broad family of inverse problems in which unknown quantities, whether initial conditions, source terms, driving forces, or other unknowns, must be recovered from space-time samples generated through the action of an evolution operator. Rather than relying on a single, densely sampled snapshot, one exploits the dynamics of the underlying system across multiple time levels to compensate for limited spatial measurements.

In this talk, we give an overview of several key problems within this framework. We discuss the initial condition recovery problem, where the iterates of a bounded operator, sampled at fixed spatial locations, give rise to frame-theoretic conditions that govern stable reconstruction. We then turn to the source recovery problem, in which an unknown driving term must be identified from the observed evolution, leading to a different but related set of operator-theoretic questions. Throughout, we highlight how spectral theory, particularly of normal operators, and frame theory provide the natural language and tools for analyzing these problems.

We will also discuss open problems and connections to related areas including sampling theory, operator algebras, and applied harmonic analysis.

Ilia Binder, Computability in Analysis and Dynamical Systems

The lecture is devoted to the role of computability theory in the study of classical objects of analysis and dynamical systems, from a perspective closely aligned with modern operator theory. The central question is deceptively simple: given an analytically well‑defined object, can it be effectively approximated by an algorithm? While existence and structural results form the backbone of functional and harmonic analysis, computability theory reveals an additional layer of complexity, distinguishing between objects that exist abstractly and those that are accessible in any constructive sense. This distinction turns out to be essential even in very regular analytical settings.
I will illustrate these ideas through several examples involving operators and invariant structures. In computable thermodynamic formalism, questions concerning the computability of pressure, equilibrium states, and invariant measures are naturally formulated in terms of transfer operators, whose spectral and asymptotic properties may exhibit fundamental non‑computability. Similar phenomena appear in harmonic analysis and in computable Carathéodory theory, where classical convergence and boundary correspondence theorems fail to admit effective counterparts. The talk will also discuss the existence of non‑computable Julia sets, showing that even when the defining dynamical system and its parameters are computable, the resulting invariant set may be algorithmically inaccessible. From the operator‑theoretic point of view, these results highlight a persistent gap between analytical control and effective realizability, and suggest computability as a unifying framework for understanding intrinsic limitations in analysis and dynamics.

Ilia Binder, Negative powers of Hilbert-space contractions

I shall discuss the following theorem, which confirms a conjecture of Jean Esterle. For each closed subset E of the unit circle of Lebesgue measure zero, there exists a positive sequence u\to\in$ with the following property: if T is a contraction on a Hilbert space such that \s(T)\s E and ||T²||=O(u²) as n\to\in, then T is a unitary operator.

Nilima Nigam, Approximation, computation and spectral geometry

Spectral geometry is concerned with the relationship between the geometric properties of a domain and the spectra of (typically elliptic) operators defined on them. Approximation theory and numerical analysis provide powerful tools to study the spectra of operators, and careful computations can lead to both insight and assistance with proofs. There is rich mathematics at the interface of numerical analysis and spectral geometry.
In this talk we explore these connections through two examples. In one, high-accuracy discretization reveals insight into the structure of the Steklov spectrum, whilst in the other example ideas from numerical analysis are used to prove a modification of Schiffer's conjecture.

William Slofstra, Decision problems for operator algebras

A nonlocal game is a simple cooperative game used to explore the power of entanglement in quantum information. The optimal winning probability of a nonlocal game turns out to be the operator norm of an element of the tensor product of two free group algebras. Can we compute this operator norm? If we instead wanted to compute the operator norm in a single copy of a free group algebra (or similar ), this would be possible by the work of Schmüdgen, Helton, McCullough, etc. However, for the tensor product of two free algebras, the MIP*=RE theorem of Ji, Natarajan, Vidick, Wright, and Yuen shows that it is undecidable to compute this operator norm, even approximately. This has opened up a landscape of questions about decision problems in operator algebras. In this talk, aimed at newcomers to the area, I'll survey what we know already, and what we'd like to know. I'll include joint work with Mehta and Zhao, the recent MIPco=coRE theorem of Lin, and hopefully lots of other results as time permits.

Joel Tropp, Stahl's theorem and random matrices

Stahl's theorem, formerly the BMV Conjecture, is a beautiful and deep fact about the monotonicity properties of the trace exponential function on self-adjoint matrices. This talk describes some elegant new applications of Stahl's theorem in the study of random matrices.

Preprints: arXiv:2501.16578 and arXiv:2603.04365.