Special sessions

Sanne ter Horst, Christian Mehl

    • Sanne ter Horst (North West University, Potchefstroom, South Africa)
    • Christian Mehl (Technishe University, Berlin, Germany)
On 1 April 2021, Andre Ran turned 65. We celebrate this fact via a special session with talks on topics that have played an important role in Andre's career, including matrix analysis in indefinite inner products, factorization of matrix functions, Riccati equations and applications to system and control theory, to name a few.

Il Bong Jung, Piotr Budzyński, Zenon Jabłoński

    • Il Bong Jung (Kyungpook National University, Daegu, Korea)
    • Piotr Budzyński (University of Agriculture, Krakow, Poland)
    • Zenon Jabłoński (Jagiellonian University, Kraków, Poland)
A relationship between Hilbert space operator theory and moment problem theory is well known. The interplay between these two gave impetus for investigations that cover a variety of topics. These include the subnormality and complete hyperexpansivity of bounded and unbounded operators, weighted shifts of various types, composition operators, positive and conditional positive definiteness of sequences etc. The session focuses on these topics and more.

Roland Duduchava, Mikhael Ruzhansky

    • Roland Duduchava (University of Georgia, Tbilisi, Georgia)
    • Mikhael Ruzhansky (University of Ghent, Belgium)
Session will host contributions in analysis on groups: function theory on groups, differential and pseudodifferential equations on groups, including convolution equations.

Nikolai Vasilevski, Jani Virtanen, Kehe Zhu

    • Nikolai Vasilevski (CINVESTAV, Mexico City, Mexico)
    • Jani Virtanen (University of Reading, Great Britain)
    • Kehe Zhu (State University of New York at Albany, NY, USA)
The interaction between analytic function spaces and operator theory is a fruitful area of modern analysis. Many problems in abstract operator theory become more approachable once the operators are unitarily transformed to analytic function spaces. A classical example is Beurling’s theorem on invariant subspaces of the unilateral shift operator. The focus of this special session is on analytic function spaces and operators acting on them. Spaces that are frequently used in operator theory include the Hardy space, the Bergman space, the Dirichlet space, and the Fock space. Operators on analytic function spaces that are extensively studied in recent years include Toeplitz operators, Hankel operators, and composition operators.

Kallol Paul, Jacek Chmieliński, Debmalya Sain

    • Kallol Paul (Jadavpur University, India)          
    • Jacek Chmieliński (Pedagogical University of Krakow, Poland)         
    • Debmalya Sain (Indian Institute of Science, India)
Banach space theory, and more generally, Functional Analysis and Operator Theory, remains an important topic in Mathematics, not the least because of its deep connections with many other branches of Mathematics and the numerous practical applications in modern day society. In recent times, various analytic methods, including but not limited to Birkhoff-James orthogonality, have been used to understand the geometry of Banach spaces. On the other hand, geometric observations in Minkowski planes have motivated several analytic notions, such as those of (left and right) symmetric points in Banach spaces and their connections with extreme contractions and isometries. This interplay between analytic and geometric ideas in the framework of Banach spaces is the main theme of our proposed session. Apart from being interesting in its own right, this particular area of research is also important from the perspectives of approximation theory and optiomization theory. The proposed session is planned to consist of the talks of some of the experts working in the broad area of geometry of Banach spaces. It is reasonable to expect that the talks to be presented at the proposed session will cover a broad spectrum of topics of current interest, thus playing a positive role in the dissemination of knowledge, exchange of ideas, and the beginning of possible future collaborations.

Michael Hartz, Felix Schwenninger

    • Michael Hartz (University od Sarland, Saarbrücken, Germany)
    • Felix Schwenninger (TU Twente, Netherlands)
The topic of this session are functional calculi, especially analytic functional calculi for Hilbert and Banach space operators in one and several variables. A particular focus lies on spectral constants and spectral sets. In recent years, there has been a surge of activity in this area. In the context of Crouzeix’s conjecture, this session aims to address recent developments in determining the optimal spectral constant for the numerical range. Moreover, we intend to cover applications of functional calculi to operator semi-groups, as well as functional calculi for operator tuples.

Andrzej Horzela, Fabio Bagarello, Stephen Bruce Sontz, Franciszek H.Szafraniec

    • Andrzej Horzela (Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland)
    • Fabio Bagarello (DEIM, University of Palermo, Italy)
    • Stephen Bruce Sontz (CIMAT Guanajuato, Mexico)
    • Franciszek H.Szafraniec (Jagiellonian University in Kraków, Poland)

William Ross, Javad Mashreghi

    • William Ross (University of Richmond, USA)
    • Javad Mashreghi (Laval University, Québec, Canada)
Model spaces, orthogonal complements of Beurling invariant subspaces for the classical shift on the Hardy space, are ubiquitous in operator theory and function theory. Indeed, in operator theory compressions of the shift to model spaces represent certain classes of Hilbert space contractions. In function theory, model spaces consist of pseudocontinuable functions and this have many fascinating properties. Recently, through work initiated by Sarason, model spaces are being explored through the lens of truncated Toeplitz operators. We propose a special session of roughly 20-25 speakers on model spaces and their close cousins the de Branges-Rovnyak spaces.

Volker Mehrmann, Arjan van der Schaft

    • Volker Mehrmann (Technical University, Berlin, Germany)
    • Arjan van der Schaft (University of Groningen, Netherlands)
Energy based modeling via port-Hamiltonian (pH) systems has become a very important feature of modern systems and control approaches. PH systems generalize Hamiltonian systems, in the sense that conservation of energy for Hamiltonian systems is replaced by a dissipation inequality. The physical properties of pH systems are encoded in the algebraic structure of the coefficient matrices and in geometric structures associated with the flow of the differential equation. This leads to a remarkably robust modeling paradigm that greatly facilitates the combination and manipulation of pH systems.  In particular, the family of pH systems is closed under power-conserving interconnection;  model reduction of pH systems via Galerkin projection yields (smaller) pH systems; and conversely, pH systems are easily extendable, allowing to increase the range of applications while ensuring that basic conservation principles remain to hold. Furthermore, pH systems have shown their versatility both for finite-dimensional and infinite-dimensional linear systems, as well as for nonlinear physical systems.
      This section will present all major aspects of pH systems, including modeling, numerical methods, control theory, operator theory and functional analysis.

Janusz Wysoczański, Vitonofrio Crismale, David Jekel

    • Janusz Wysoczański (Wroclaw University, Poland)
    • Vitonofrio Crismale (University of Bari, Italy)
    • David Jekel (University of California, San Diego, USA)

In this Session we intend to present recent developments in the wide area of noncommutative probability and their applications to operator algebras and in operator theory. Noncommutative probability is based on various notions of independences, which are meaningful for elements of arbitrary *-algebras. These notions include freeness of Voiculescu, monotone independence of Muraki, Boolean independence and mixtures of them. Models of such independences are given by algebras generated by creation and annihilation operators acting on various deformations of the full Fock space, which produce new interesting examples of operator algebras to investigate. On the other hand, classical properties enjoyed by commutative random variables are also generalized to these noncommutative settings. This includes studies of various convolutions of probability measures described by appropriate moment-cumulant relations. Deformations of measures and convolutions can be generalized to the level of operators, which leads to new results in operator theory.

Jurij Volcic, James Eldred Pascoe

    • Jurij Volcic (University of Copenhagen, Denmark)
    • James Eldred Pascoe (University of Florida, USA)
Advancements in noncommutative function theory, noncommutative real algebraic geometry and related topics will be discussed.Related topics may include the algebriac theory of free skew fields, quantum information theory, optimization, matrix convexity,and systems and control.

Ilya Spitkovsky, Thomas Schulte-Herbrüggen

    • Ilya Spitkovsky (New York University Abu Dhabi, United Arab Emirates)
    • Thomas Schulte-Herbrüggen (Technische Universität München, Germany)
We aim to bring together both researchers working on the properties of the numerical range per se (its shape and explicit description for various classes of structured matrices and operators), its various generalizations (higher rank, normalized, maximal, etc.), and applications to quantum and statistical mechanics, quantum information and computation, numerical methods, and its connections to operator theory. A special emphasis will be put on the results stemming from Kippenhahn's work (Kippenhahn polynomials, Kippenhahn curves).

Tomasz Kania, Niels Laustsen, Kevin Beanland

    • Tomasz Kania (Jagiellonian University in Kraków, Czech Academyof Sciences)
    • Niels Laustsen (Lancaster University, United Kingdom)
    • Kevin Beanland (Washington & Lee University, USA)
A session dedicated to recent progress in the study of bounded operators on Banach spaces, especially the significant results obtained in the last few years concerning the number of closed ideals of the Banach algebra of bounded operators acting on a Banach space.

Petru Cojuhari, Aurelian Gheondea

    • Petru Cojuhari (AGH University of Technology Kraków, Poland)
    • Aurelian Gheondea (Bilkent University, Ankara, Turkey, "Simion Stoilow" Institute of Mathematics, Romania)
The session "Operator Theory and Mathematical Physics" will focus on current developments in operator theory and its applications to problems of mathematical physics, quantum mechanics, quantum field theory and other related fields. The main goal is to invite experts to present their latest advances in operator theory techniques that are related to mathematical physics problems as well as to point out operator theory problems for future research.

David Kribs, Karol Życzkowski

    • David Kribs (University of Guelph, Canada)
    • Karol Życzkowski (Jagiellonian University Kraków, Poland)
Over the last two decades, techniques and tools from operator and matrix theory have played an increasingly important role in quantum information theory. This session will include talks from speakers who work at the intersection of operator theory and quantum information theory.

Elias Katsoulis, Matthew Kennedy

    • Elias Katsoulis (East Carolina University, USA)
    • Matthew Kennedy (University of Waterloo, Canada)
The theory of operator systems and operator spaces originates in work of Stinespring and Arveson from the sixties. The theory has subsequently experienced remarkable growth, and has found significant applications in operator algebras and beyond. Arveson's original goal was the development of an abstract framework for dilation theory, along with a corresponding theory of boundaries for operator algebras. A complete realization of this goal took many years to fully materialize, and required deep work by numerous mathematicians. A crucial development was Hamana's introduction of injective envelopes for operator systems, along with his corresponding proof of the existence of the C*-envelope. These ideas have recently found exciting new applications, for example to the ideal structure of operator algebras arising from noncommutative dynamics, to the Hao-Ng isomorphism problem, and to the study of co-universal C*-algebras algebras. The purpose of this special session is to provide a detailed picture of the many applications of operator space techniques in operator algebras, and to bring together practitioners within these diverse areas.

Daniel Alpay, Paula Cerejeiras, Fabrizio Colombo

    • Daniel Alpay (Chapman University, California, USA)
    • Paula Cerejeiras (University of Aveiro, Portugal)
    • Fabrizio Colombo (Politecnico di Milano, Italy)
The theory of operator systems and operator spaces originates in work of Stinespring and Arveson from the sixties. The theory has subsequently experienced remarkable growth, and has found significant applications in operator algeClifford analysis, and more generally hypercomplex analysis, is an emergent field with a wide range of applications, from quantum mechanics to modern signal processing. As such it plays an increasingly important role, and deserves a central place in IWOTA meetings. It is dedicated to the extension of classical analysis to non-commutative structures while focusing on the study of functions belonging to the null-space of a Dirac operator. This session aims to invite experts to present their latest advances related to Operator Theory in Clifford analysis, as well as its applications to physics, numerical analysis of PDEs, development of a spectral theory for quaternion operators, linear systems, and others.

Jochen Glück, Henrik Kreidler

    • Jochen Glück (University of Passau, Germany)          
    • Henrik Kreidler (University of Wuppertal, Germany)
        Positivity plays a major role in modern operator theory. In this session we aim to discuss two major developments which have been in the focus of recent research.       
  • In the theory of dynamical systems, techniques that employ the so-called Koopman operator of the system - a positive linear operator on an infinite dimensional space which encodes all information of the underlying non-linear system - plays an increasingly prominent role. It allows to approach topological, measure-preserving and smooth dynamics from an operator theoretic perspective.
  • The asymptotic behavior of operators and operator semigroups is much more accessible under the assumption of positivity (which is automatically fulfilled in many applications). A variety of new methods have been developed to study the long-term behavior of positive one-parameter operator semigroups. We intend to discuss recent progress in these topics, and to identify and highlight possible connections to other fields.

John E. McCarthy, Łukasz Kosiński

    • John E. McCarthy (Washington University, St. Louis, USA)
    • Łukasz Kosiński (Jagiellonian University, Kraków, Poland)

Christiane Tretter

    • Christiane Tretter (Bern University, Switzerland)

The spectral theory of non-selfadjoint operators has seen steadily growing interest in the last decades for at least two reasons. Firstly, non-selfadjoint operators are ubiquitous in mathematical physics, starting from classical fields such as resonances in quantum mechanics over damped wave equations in elasticity theory, flows of viscous compressible fluids in hydrodynamics to highly topical areas such as photonics and phononics. Secondly, non-selfadjoint operators exhibit a rich variety of surprising phenomena and pose interesting new challenges, such as unpleasant resolvent growth, high sensitivity of spectra to perturbations, spectral pollution outside of essential spectral gaps or spectral invisibility  in numerical approximations. This special session is dedicated to recent developments in this exciting area of operator theory and its applications.

Raul Curto

    • Raul Curto (University of Iowa, Iowa, USA)
Over the last two decades, a myriad of new and exciting results have been obtained in the field of moment problems, and significant applications to various areas of pure and applied mathematics have been obtained. The Special Session will aim at bringing some of the top contributors to present cutting-edge research, and to stir renewed interest in these topics.
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