IWOTA Lancaster 2020: International Workshop on Operator Theory and its Applications to be held at Lancaster from 17th to 21st August 2020

Lead Research Organisation: Lancaster University
Department Name: Mathematics and Statistics

Abstract

Operator theory has developed alongside electrical engineering and control theory. An early application of advanced analysis to communications is Whittaker's sampling theorem from 1908.

In the 1970s, political and cultural factors inhibited the exchange of ideas between mathematicians and engineers in Eastern Europe and Western countries. In 1981, J. W. Helton founded the International Workshop on Operator Theory and Applications as a satellite of the Mathematical Theory of Network and Systems. Since then, IWOTA has grown and has become established as a major scientific organization in operator theory, that holds annual meetings with regular participants who guide the development of the subject through their publications and involvement in scientific journals. In 2004, the EPSRC supported the only previous meeting of IWOTA in the UK, at Newcastle. Recently, operator theory has grown in China, as evidenced by the IWOTA in Shanghai in 2019 with 352 participants. Israel Gohberg was the driving force behind the development of IWOTA, and Gohberg's scientific legacy will be honoured by a memorial lecture at Lancaster by Vern Paulsen of the Institute of Quantum Computing at the University of Waterloo in Canada.

In August 2020, MTNS is holding its biennial meeting in Cambridge. It is therefore opportune for IWOTA to meet in the United Kingdom, and for analysts in the UK to reassert their position at the forefront of the subject, and strengthen their links with colleagues in USA, India, Europe and China.

Scientific organization
The local organizing committee for this workshop includes members from Lancaster, Newcastle and King's College London, have the largest groups of analysts in the UK, with 26 academic staff. The IWOTA steering committee consists of senior mathematicians who have organized previous workshops. Following detailed discussions between the PI and the IWOTA convenor J. W. Helton in Shanghai, the IWOTA Steering Committee approved the scientific agenda in this proposal. The organizers of special sessions were selected according to their willingness to create a coherent and attractive agenda of research activity and talks.


The scientific agenda is based upon Special Sessions at which participants will consider specific aspects of operator theory and its applications. From the suggested talks by participants, the Special Session Leaders will select titles for talks and abstracts in advance of the meeting. The topics have been selected by the local organizers in conjunction with the IWOTA Steering Committee so as to develop further the success of previous special sessions on established topics and stimulate progress on newly emerging topics. This will stimulate the development of operator theory within the UK.

The UK already has established research groups in spectral theory for differential operators and operator algebras, and we expect that UK researchers will play a prominent role in these sessions. However, the UK has not yet developed research groups in topics such as free algebraic geometry, and the workshop will help to raise awareness of these new areas and create new opportunities for research, particularly for early career researchers from the UK.

The plenary and semi plenary speakers are established experts on topics related to the special sessions. They have been chosen from several countries, reflecting the importance of operator theory as a scientific endeavour and the international character of the workshop.

SPECIAL SESSIONS

Operator spaces, quantized function theory and noncommutative Lp spaces
Operator algebras
Operator algebras in quantum theory
Noncommutative probability and Random Matrices
Operator semigroups and functional calculus
Spectral theory for differential operators
Operators on analytic function spaces and related applications
Hilbert space operator theory and complex geometry
Free algebraic geometry
Emerging topics
Early Career Researchers

Planned Impact

Operator theory provides the technical basis for the study of linear systems. Linear systems are often specified by operators or by their transfer functions; both these topics are of central concern to IWOTA. As such there are applications to the stability and control of power networks. Distributed parameter systems have infinite-dimensional state spaces and are analysed via semigroups of operators on Hilbert space, as in themes (5) Operator semigroups and functional calculus and (6) Spectral theory and differential equations.


Digital signal processing of data transmitted by wireless networks is an aspect of the EPRSC portfolio which is important in this age of mobile broadband use. Random matrix theory is employed to study Multiple-Input Multiple-Output models for transmission between multiple transmitting antennae and multiple receivers. The theoretical foundation for this model was proposed by E. Telatar (Bell Labs) in Transaction on Emerging Telecommunications Technologies 10 (1999), 585-595. This relates to theme (4) Noncommutative probability and random matrices. Another important application of MIMO is in power transmission in smart distribution grids.

Theme 9 Free algebraic geometry is being developed with a view to applications in control engineering. Every problem in linear systems engineering which is given entirely by a signal flow diagram and features L2 specification on its signals is equivalent to giving noncommuting polynomials and finding solutions to certain "inequalities" involving these polynomials.

Operator methods in geometric rigidity theory have application to crystallography, such as the study of infinite bond-node frameworks and their surface modes. This relates to theme 10: Emerging topics.

Publications

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Bischoff M (2022) Galois Correspondence and Fourier Analysis on Local Discrete Subfactors in Annales Henri Poincaré

 
Description Report on the Meeting IWOTA Lancaster UK 2021

Originally IWOTA Lancaster was scheduled for 2020, but was postponed until 2021 and was held as an online event. On Monday 13th August, the Deputy Vice-Chancellor of Lancaster University Steve Bradley and the Vice President of IWOTA Igor Klepp opened the meeting by welcoming over 270 participants from 37 countries to IWOTA. The meeting thus achieved the stated aim of bring together researchers from Europe, America and Asia to a meeting based in the UK. The participants included over 107 early career researchers. The workshop was intended to enhance the career development and provide opportunities for early career researchers, and this was realised through their active participation and involvement in organizing the Special Sessions 7 and 11.


The meeting featured Special Sessions on the following topics.


1 Operator spaces, quantized function theory and noncommutative Lp spaces
Organizers : David Blecher and Christian Le Merdy

2 Operator algebras
Organizer: Joachim Zacharias (Glasgow)

3 Operator algebras in quantum theory
Organizers: Jason Crann (Carleton University, Canada) and Ivan Todorov.

4 Noncommutative probability and Random Matrices
Organizers: Jani Virtanen (Reading) and Kenneth Dykema (TAMU)

5 Operator semigroups and functional calculus
Organizers: Markus Haase (Kiel) and Yuri Tomilov (IMPAN, Warsaw)

6 Spectral theory and differential operators
Organizers: Ian Wood (Kent), Malcolm Brown (Cardiff), Andrii Khrabustovskyi, (Graz University of Technology, Austria);

7 Operator theory and communications
Organizer: Lucinda Hadley (Lancaster)

8 Hilbert space operator theory and complex geometry
Organizers: Tirthankar Bhattacharyya (IISc Bangalore) and Lucasz Kosinski (Jagiellonian University, Krakow)

9 Free algebraic geometry and free analysis
Organizers: Victor Vinnikov (Ben Gurion) and Juric Volcic (TAMU)

10 Emerging topics: from Operator Algebras to Geometric Rigidity
A special session of IWOTA to mark the retirement of Professor Stephen C. Power from Lancaster University.
Organizers Derek Kitson (Mary Immaculate College), Rupert Levene (University College Dublin)

11 Early Career Researchers
Organizers: Elefteris Kastis and Maria Eugenia Celorrio (Lancaster).

12 Quantum groups and algebraic quantum field theory
Organizers: Uwe Franz (Besancon) and Robin Hillier (Lancaster)

13 Linear systems (cancelled)

14 Multivariable operator theory
Organizers: Greg Knese (Washington) and Michael Dritschel (Newcastle, UK)

15 Complex Analysis and Operator Theory
Organizers: Kehe Zhu (Albany) and Jani Virtanen (Reading)

16 Operator Ideals and Operators on Banach spaces
Organizers: Niels Laustsen, Tomasz Kania, Kevin Beanland

Main Lectures
The starred talks are available to the general public as videos on the YouTube channel IWOTA Lancaster
https://www.youtube.com/playlist?list=PLfyDC3Q5UAvMJNKPtLKFw-OuVqaeQFoCO

Monday 16th August
*Charles Batty: Bounded functional calculi for unbounded operators*
Birgit Jacob: Controllability and Riesz bases of infinite-dimensional port-Hamiltonian systems
*Victor Vinnikov: A Beurling-type theorem for indefinite Hardy spaces on finite bordered Riemann surfaces*
*Hakan Hedenmalm: Planar orthogonal polynomials and soft Riemann--Hilbert problems*

Tuesday 17th August
*Benoit Collins: On the norm convergence of multi-matrix random matrix models*
*Magdalena Musat: Factorizable quantum channels, non-closure of quantum correlations and the Connes embedding problem*
*Zhengwei Liu: Quantum Fourier analysis*
Kenneth Dykema: Spectral decompositions in finite von Neumann algebras

Wednesday 18th August
*John E. McCarthy: Complete Pick spaces-what are they, and why are they interesting?*
*Raul Curto: The Beurling--Lax--Halmos theorem for infinite multiplicity*
*Mihai Putinar: Finding the cloud of a 2D point distribution*
*Zinaida Lykova: The mu -synthesis interpolation problem and some associated domains*

Thursday 19th August
The Israel Gohberg Lecture was founded to commemorate the scientific achievements of Israel Gohberg, who was a driving force behind IWOTA. The inaugural lecture was by *Vern Paulsen: Cooperative games and entanglement*
*Christian Le Merdy: ell^1 bounded maps and S^1 bounded maps on noncommutative L^p spaces*
*Juric Volcic: Positive noncommutative rational functions*
*Fritz Gesztesy: The limiting absorption principle and continuity properties of the spectral shift function for massless Dirac type operators*

Friday 20th August
*Daniel Alpay: Discrete analytic functions and Schur analysis*
*Omar El Fallah: Singular values of Hankel operators on Bergman spaces*

The technical production of the talks was by Waggle Events. The UK Engineering and Physical Sciences Research Council supported the meeting via grant EP/T007524/1 IWOTA Lancaster UK 2021, principal investigator Gordon Blower, co investigators Stephen Power and Derek Kitson. The local administration was by Anna Barnett and Stephanie Kutschmann. The organizers intend to publish conference proceedings in the series Operator Theory: Advances and Applications, published by Birkhauser. The editors are Yemon Choi (Lancaster), Gordon Blower (Lancaster) and Matt Daws (UCLAN).
Exploitation Route The meeting will stimulate research in particular topics in the UK, such as free algebraic geometry and algebraic quantum field theory.

There are potential applications to communications engineering, particularly wireless transmission.
Sectors Digital/Communication/Information Technologies (including Software),Education

 
Description Report on the Meeting IWOTA Lancaster UK 2021 Originally IWOTA Lancaster was scheduled for 2020, but was postponed until 2021 and was held as an online event. On Monday 13th August, the Deputy Vice-Chancellor of Lancaster University Steve Bradley and the Vice President of IWOTA Igor Klepp opened the meeting by welcoming over 270 participants from 37 countries to IWOTA. The meeting thus achieved the stated aim of bring together researchers from Europe, America and Asia to a meeting based in the UK. The participants included over 107 early career researchers. The workshop was intended to enhance the career development and provide opportunities for early career researchers, and this was realised through their active participation and involvement in organizing the Special Sessions 7 and 11.
First Year Of Impact 2021
Sector Digital/Communication/Information Technologies (including Software),Education
 
Description IWOTA Youtube 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Creation of a YouTube channel to distribute main lectures from scientific meeting
Year(s) Of Engagement Activity 2021
URL https://www.youtube.com/watch?v=apzqliOhYHY