Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications
WHT
5 August 2019 to 30 August 2019
Programme theme
The Wiener-Hopf technique enables us to solve numerous physical problems motivated by real world applications modelled, for example, by partial differential equations and stochastic processes. The Wiener-Hopf technique is currently used in a wide range of disciplines including acoustics, finance, Lèvi processes, hydrodynamics, elasticity, potential theory and electromagnetism.
The theory of scalar Wiener-Hopf equations is now very rich and well developed. In contrast, much less is known about matrix Wiener-Hopf equations. These are a natural extension of the scalar case, and enable us to model more advanced problems. As it stands, solutions to matrix Wiener-Hopf problems have to be constructed on a case-by-case basis, or in an approximate fashion. The focus of this programme will be on matrix Wiener-Hopf equations, constructive numerical methods and applications. The three main aims will be:
- Matrix factorisation, approximate methods and their numerical implementation.
There are numerous approximate methods for Wiener-Hopf matrix factorisation. However, there is no clear picture for deciding when a method is appropriate or numerically efficient. Consequently, approximate Wiener-Hopf factorisation is highly specialised and a difficult subject for non-experts. An important outcome of the programme will be to make this more routine by filling the outstanding gaps in the literature. There is also a lot of scope for the theoretical study of methods motivated by applications. This requires a close collaboration between mathematicians from the pure and applied communities. Developing existing methods into working algorithms and making them freely available in a toolbox will make the Wiener-Hopf technique more easily accessible for applications than is currently the case.
- Establishing links between different applications of the Wiener-Hopf method.
There are several disjoint communities who rely on the Wiener-Hopf method, and developments in one field often go unnoticed in another. There is much to be gained by generalising the developments in one area to solve open problems in other areas.
- Consolidating existing knowledge and developing a set of promising new directions.
We will consider the area as a whole, pose open problems and map out promising directions. This will highlight new developments and applications, and make the area more attractive to young researchers.
The above aims will be achieved by bringing together internationally leading experts in the Wiener-Hopf technique from diverse areas and catalyse new interactions between them. There will be an emphasis on enabling young researchers to meet and interact with established experts.
Click here to download the programme's final scientific report
WHT programme: interview with organisers Anastasia Kisil, Ian Thompson and Gennady Mishuris
Workshops
Factorisation of matrix functions: New techniques and applications
12 August 2019 to 16 August 2019
WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method
1 July 2024 to 5 July 2024
Seminars
| Tuesday 6th August 2019 | |||
|---|---|---|---|
| 09:00 to 10:15 |
David Abrahams Isaac Newton Institute |
Room 1 | 
|
| 10:30 to 11:45 |
David Abrahams Isaac Newton Institute |
Room 1 |
|
| 12:00 to 13:15 |
Andrey Shanin Moscow State University ; Raphael Assier University of Manchester |
Room 1 |
|
| 14:15 to 15:30 |
Michael Nieves Keele University |
Room 1 | |
| 15:45 to 17:00 |
Alexey Kuznetsov York University (Canada) |
Room 1 |
|
| Wednesday 7th August 2019 | |||
|---|---|---|---|
| 09:00 to 10:15 |
Andrey Shanin Moscow State University ; Raphael Assier University of Manchester |
Room 1 |
|
| 10:30 to 11:45 |
Guido Lombardi Politecnico di Torino ; J.M.L. Bernard ENS de Cachan |
Room 1 |
|
| 12:00 to 13:15 |
Sheehan Olver Imperial College London |
Room 1 |
|
| 14:15 to 15:30 |
David Abrahams Isaac Newton Institute |
Room 1 |
|
| 15:45 to 17:00 |
Frank Speck Universidade de Lisboa |
Room 1 | |
| Thursday 8th August 2019 | |||
|---|---|---|---|
| 09:00 to 10:15 |
Frank Speck Universidade de Lisboa |
Room 1 | |
| 10:30 to 11:45 |
Guido Lombardi Politecnico di Torino ; J.M.L. Bernard ENS de Cachan |
Room 1 | |
| 12:00 to 13:15 |
Andrey Shanin Moscow State University ; Raphael Assier University of Manchester |
Room 1 |
|
| 14:15 to 15:30 |
Guido Lombardi Politecnico di Torino ; J.M.L. Bernard ENS de Cachan |
Room 1 |
|
| 15:45 to 17:00 |
Alexey Kuznetsov York University (Canada) |
Room 1 |
|
| Friday 9th August 2019 | |||
|---|---|---|---|
| 09:00 to 10:15 |
Andrey Shanin Moscow State University ; Raphael Assier University of Manchester |
Room 1 |
|
| 10:30 to 11:45 |
Guido Lombardi Politecnico di Torino ; J.M.L. Bernard ENS de Cachan |
Room 1 |
|
| 12:00 to 13:15 |
Sheehan Olver Imperial College London |
Room 1 |
|
| 14:15 to 15:30 |
Michael Nieves Keele University |
Room 1 | |
| 15:45 to 17:00 |
Frank Speck Universidade de Lisboa |
Room 1 | |
| Friday 23rd August 2019 | |||
|---|---|---|---|
| 15:00 to 15:30 |
Matthew Nethercote University of Manchester |
Room 2 |
|
| 15:30 to 16:00 |
Peter Baddoo University of Cambridge |
Room 2 | |
| Wednesday 28th August 2019 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Andrey Shanin Moscow State University |
Room 2 |
|
Organisers
- Vito Daniele Politecnico di Torino
- Anastasia Kisil University of Cambridge
- Guido Lombardi Politecnico di Torino
- Gennady Mishuris Aberystwyth University
- Ian Thompson University of Liverpool
Speakers
- David Abrahams Isaac Newton Institute
- Raphael Assier University of Manchester
- Peter Baddoo University of Cambridge
- J.M.L. Bernard ENS de Cachan
- Alexey Kuznetsov York University (Canada)
- Guido Lombardi Politecnico di Torino
- Matthew Nethercote University of Manchester
- Michael Nieves Keele University
- Sheehan Olver Imperial College London
- Andrey Shanin Moscow State University
- Frank Speck Universidade de Lisboa
Participants
- David Abrahams Isaac Newton Institute
- Victor Adukov South Ural State University
- Nataliia Adukova South Ural State University
- Raphael Assier University of Manchester
- Lorna Ayton University of Cambridge
- Peter Baddoo University of Cambridge
- David Baker University of Cambridge
- J.M.L. Bernard ENS de Cachan
- Aloknath Chakrabarti Indian Institute of Science
- John Chapman Keele University
- Matthew Colbrook University of Cambridge
- Marina Dubatovskaya Belarusian State University
- Roland Duduchava Tbilisi State University; University of Georgia
- Lasha Ephremidze Tbilisi State University; New York University
- Nikolai Gorbushin ESPCI ParisTech
- Xun Huang Peking University; Hong Kong University of Science and Technology
- Justin Jaworski Lehigh University
- Anastasia Kisil University of Cambridge
- Alexey Kuznetsov York University (Canada)
- Andreas Kyprianou University of Bath
- Jane Lawrie Brunel University
- Pavlos Livasov Aberystwyth University
- Guido Lombardi Politecnico di Torino
- Elena Luca University of California, San Diego
- Mikhail Lyalinov Saint Petersburg State University
- Georg Maierhofer University of Cambridge
- Mike Meylan University of Newcastle, Australia
- Gennady Mishuris Aberystwyth University
- Natasha Movchan University of Liverpool
- Alexander Movchan University of Liverpool
- Matthew Nethercote University of Manchester
- Michael Nieves Keele University
- Sheehan Olver Imperial College London
- Nigel Peake University of Cambridge
- Malte Peter Universität Augsburg
- Andrea Piccolroaz University of Trento
- Dmitry Ponomarev Vienna University of Technology; Steklov Mathematical Institute, Russian Academy of Sciences
- Marco Poort University of Illinois at Chicago; Google
- Sergei Rogosin Belarusian State University
- Andrey Shanin Moscow State University
- Eugene Shargorodsky King's College London
- Leonid Slepyan Tel Aviv University
- Frank Speck Universidade de Lisboa
- Ilya Spitkovsky New York University; College of William and Mary
- Ian Thompson University of Liverpool
- Konstantin Ustinov Institute for Problems in Mechanics of Russian Academy of Sciences
- John Raymond Willis University of Cambridge
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