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

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

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.