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.