IWOTA - International Workshop
on Operator Theory and its Applications
Une conférence satellite de l'ICM, 3-7 août 2026
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Sessions
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Programme
Liste des sessions scientifiques
Sessions scientifiques
Block Toeplitz and Hankel Operators
Organisateurs : Raul Curto (University of Iowa, USA), In Sung Hwang (Sungkyunkwan University, South Korea), Woo Young Lee (Korea Institute for Advanced Study, South Korea)
Contact des organisateurs : Raul Curto, raul-curto@uiowa.edu
Block Toeplitz and Hankel operators are canonical models for the study of bounded linear operators. They are simple enough to analyze deeply, yet rich enough to encode fundamental phenomena across pure and applied mathematics, serving as a unifying framework that connects operator theory, harmonic and complex analysis, linear algebra, mathematical physics, and engineering applications, while continually inspiring new methods, discoveries, and interdisciplinary insights. On the other hand, the study of block Toeplitz and Hankel operators naturally gives rise to the investigation of vector-valued function theory. The virtue of a vector-valued function theory lies in the fact that it assists in better understanding the scalar-valued world. This is analogous to how certain features are better visible in 2-dimensions when viewed from a 3-dimensional perspective. One prominent example is the Nagy-Foias model theory, which says that roughly speaking, every bounded linear operator in the scalar-valued world is nothing but a shadow of a "Toeplitz action" in the vector-valued world. In recent years, research in this field has been highly active, giving rise to a wide range of significant applications. This session aims to bring together experts and early career researchers to discuss and exchange recent progress and future directions in research on (block) Toeplitz, Hankel, and model operators, as well as related topics.
Dynamical sampling
Organisateurs : Roza Aceska (Ball State University, USA), Akram Aldroubi (Vanderbilt University, USA), Alex Powell (Vanderbilt University, USA)
Contact des organisateurs : Roza Aceska, raceska@bsu.edu
Dynamical sampling addresses the problem of recovering a signal from generalized samples of its orbits under the action of an evolution operator. Dynamical sampling has close connections with frame theory, harmonic analysis, approximation theory, system identification, signal processing, control theory, and dynamical systems. This session will explore recent advances in dynamical sampling.
Evolution Equations, Operator Semigroups and Applications
Organisateurs : Christian Budde (University of Free State’ South Africa)
Contact des organisateurs : Christian Budde, BuddeCJ@ufs.ac.za
This special session aims to bring together researchers to explore the vibrant interplay between abstract operator theory and the analysis of dynamic systems. At its core, the theory of operator semigroups provides a powerful and unifying framework for investigating diverse evolution equations that arise across the sciences, from quantum mechanics and fluid dynamics to population biology and financial mathematics. The field is currently experiencing a period of remarkable growth, with recent advancements deepening our understanding of asymptotic behavior, stability, and perturbation theory, while also addressing increasingly sophisticated applied challenges. This session will foster a productive dialogue on these developments, bridging the gap between pure analysis and real-world applications. We welcome contributions on a wide range of topics, including asymptotic behavior of semigroups, control theory, delay equations, evolution equations on graphs, numerical methods, port-Hamiltonian systems, positivity, and spectral theory, among others.
Free Probability
Organisateurs : Serban Belinschi (Queen’s University, Canada & CNRS, France), Ian Charlesworth (Cardiff University, UK)
Contact des organisateurs : Serban Belinschi, belinsch@queensu.ca, (Serban.Belinschi@math.univ-toulouse.fr) & Ian Charlesworth, CharlesworthI@cardiff.ac.uk
This session will feature new developments in free (and more generally, non-commutative) probability and its connections to operator theory, operator algebras, random matrices, and their applications. Recent developments concerning generalizations/extensions of freeness (freeness with amalgamation, bi-freeness, graph independence, infinitesimal freeness etc.), asymptotic freeness results and their applications, connections to mathematical logic, applications of analytic functions tools in free probability, and connections to operator spaces will be of significant interest. Various applications of free probability and random matrix theory to quantum information theory, non-commutative optimization, and mathematical physics will be highlighted.
Function Spaces and Operator Theory
Organisateurs : Zelijko Cuckovic (University of Toledo, USA), William T. Ross (University of Richmond, USA)
Contact des organisateurs : William T. Ross, wross@richmond.edu
This session will focus on properties of bounded linear operators on Hilbert and Banach spaces of analytic functions in one and several variables.
Invariant Subspaces and Cyclicity
Organisateurs : Christopher Felder (University of South Florida, USA), Bartosz Malman (Mälardalen University, Sweden)
Contact des organisateurs : Christopher Felder, felderc@usf.edu
This session brings together recent advances in the study of invariant subspaces and cyclic vectors. Topics will include structural and spectral properties of operators with rich invariant subspace lattices, criteria for cyclicity, and connections to function theory, complex analysis, and operator models. Emphasis will be placed on both classical settings (e.g., one-variable Hilbert and Banach spaces of analytic functions) and emerging contexts, including multivariable and non-commutative operator theory. Contributions from both theoretical and applied perspectives are welcome.
Matrix Analysis and Applications
Organisateurs : Dominique Guillot (University of Delaware, USA), Prateek Kumar Vishwakarma (Université Laval, Canada)
Contact des organisateurs : Dominique Guillot, dguillot@udel.edu
Matrix Analysis encompasses many central topics, including singular values and eigenvalues, numerical ranges, decompositions, inequalities, majorization, and tensor analysis. Ideas from this field have wide-ranging applications in areas such as optimization, numerical analysis, geometry, positivity, quantum information, data science, random matrix theory, and operator theory. This special session will feature talks on several of these themes, presented by experts and with the aim of fostering collaboration among scholars with shared interests.
Multivariable Operator Theory
Organisateurs : Sanne ter Horst (North-West University, South Africa), Jaydeb Sarkar (Indian Statistical Institute, India), Rongwei Yang (University at Albany, SUNY, USA)
Contact des organisateurs : Sanne ter Horst, sanne.terhorst@nwu.ac.za
In this session we bring together presentations on recent work in the wide area of multivariable operator theory. This area encompasses a range of topics, including, but not limited to, tuples of operators and functional calculus, operators associated with classes of functions in several variables, such as Hankel and Toeplitz operators, non-commutative function theory, multivariable interpolation and multidimensional systems.
Noncommutative Analysis and Ring Theory
Organisateurs : Beeri Greenfeld (Hunter College at the City University of New York, USA), Eli Shamovich (Ben-Gurion University of the Negev, Israel)
Contact des organisateurs : Eli Shamovich, shamovic@bgu.ac.il
The recent development of noncommutative analysis has, in particular, introduced new ideas from ring theory into the study of operator algebras and free function theory. For example, the noncommutative localization theory of Amitsur and Cohn saw new applications in free probability. The session's goal is to bring together experts in noncommutative analysis and pure algebraists to foster communication between the two communities.
Operator and Function Theory
Organisateurs : Pamela Gorkin (Bucknell University, USA), Thomas Ransford (Université Laval, Canada)
Contact des organisateurs : Pamela Gorkin, pgorkin@bucknell.edu
In this session, we study the ways in which functions can be used to define and study properties of operators, as well as the information we obtain about functions from associated operators. We will consider recent progress on the relation between functions and operators, including open problems such as Crouzeix's conjecture and the invariant subspace problem.
Operator Theory and Hypercomplex Analysis
Organisateurs : Daniel Alpay (Chapman University, USA), Kamal Diki (Universiteit Gent, Belgium), Uwe Kaehler (University of Aveiro, Portugal), Irene Sabadini (Politecnico di Milano, Italy)
Contact des organisateurs : Irene Sabadini, irene.sabadini@polimi.it
Hypercomplex analysis is an emergent field dedicated to the extension of classical complex analysis to non-commutative structures. This session aims to invite experts in this field to present their latest advances related to operator theory, as well as its applications to physics, analysis of PDEs, inverse problems, spectral theory based on the S-spectrum, reproducing kernel methods and Schur analysis in the hyperholomorphic setting. Relevant contributions to infinite dimensional analysis as well as applications to machine learning and probability theory are also welcome.
Quantum Information and Games
Organisateurs : William Slofstra (University of Waterloo, Canada), Jurij Volcic (University of Auckland, New Zealand)
Contact des organisateurs : Jurij Volcic, jurij.volcic@auckland.ac.nz
This session focuses on the mathematical foundations of quantum information science. The talks will highlight connections between quantum information and representation theory, operator algebras, complexity theory, polynomial optimization, and other areas of mathematics.
Real Algebraic Geometry, Moment Problems and Applications
Organisateurs : Salma Kuhlmann (University of Konstanz, Germany), Aljaz Zalar (University of Ljubljana, Slovenia)
Contact des organisateurs : Salma Kuhlmann, salma.kuhlmann@uni-konstanz.de
Real algebraic geometry (RAG), which traces its origins to Hilbert’s 17th problem from 1900, studies certificates of positivity—known as Positivstellensätze—that characterize when a polynomial is positive on the positivity sets of other polynomials. The moment problem (MP) is a classical question in functional analysis that has been investigated since the late 19th century, first appearing in a memoir by Stieltjes in 1894. The connection between RAG and the MP was established by Haviland’s Theorem (1935), which asserts that positive linear functionals on polynomials are in one-to-one correspondence with positive Borel measures. Both RAG and the MP have applications across numerous branches of mathematics, including polynomial optimization, probability and statistics, operator theory, and the theory of differential equations. In recent years, various extensions of RAG and the MP have been explored. The classical Sum of Squares (SOS) certificate of positivity, which is certified by Semi Definite Programing (SDP), has been extended to new certificates such as Sum of Nonnegative Circuit Polynomials (SONC) certified e.g. by Relative Entropy Programing (REP), or Geometric Programing. Generalizations to noncommutative versions (in matrix and operator settings), infinite-dimensional moment problems on arbitrary commutative algebras, and others have been found and exploited. This session aims to present some of the latest results, both in the classical setting and its extensions.
Spectral Theory and Differential Operators
Organisateurs : Jussi Behrndt (Graz University of Technology, Austria), Carsten Trunk (Technische Universität Ilmenau, Germany)
Contact des organisateurs : Jussi Behrndt, behrndt@tugraz.at
Spectral theory of differential operators is a rapidly developing area on the edge between differential equations, mathematical physics, and functional analysis, with applications in many branches of mathematics, mathematical physics and theoretical physics. The main objective of this session is to discuss various recent developments in this branch of operator theory and its applications.
Tensors and their Applications
Organisateurs : Shmuel Friedland (University of Illinois, Chicago, USA), Benjamin Lovitz (Concordia University, Canada)
Contact des organisateurs : Shmuel Friedland, friedlan@uic.edu
Tensors are ubiquitous in the following fields: biology-DNA microarrays; computer science-fast matrix multiplications;engineering-tensor decomposition for signal processing and machine learning; mathematics-border rank and secant varieties; quantum physics-entanglement and separability. In this session we will bring experts who will present recent developments in these and related fields.
Transfer operator and thermodynamic formalism
Organisateurs : Ilia Binder (University of Toronto, Canada), Zhiqiang Li (Peking University, China)
Contact des organisateurs : Zhiqiang Li, zli@math.pku.edu.cn
The scientific session "Transfer Operator and Thermodynamic Formalism" will bring together leading mathematicians from related fields to explore the vibrant and rapidly evolving landscape of interconnected domains of research surrounding transfer operators and thermodynamic formalism. Thermodynamic formalism, born from the synergy of statistical mechanics and dynamical systems, provides a powerful statistical description of chaotic systems. At its heart lies the transfer operator, a central tool that encodes the ergodic and geometric properties of a dynamical system through its spectral data. This framework has proven remarkably versatile, yielding profound insights into invariant measures, the decay of correlations, entropy, and the zeta functions of dynamical systems. This scientific session aims to foster a collaborative environment to discuss recent breakthroughs and future challenges. We will explore the deep connections to geometry, particularly in the study of hyperbolic and conformal systems, and examine the growing interface with probability.