Factorisation of matrix functions: New techniques and applications

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Workshop theme

The Wiener–Hopf method has been interdisciplinary ever since its inception. It resulted from a collaboration between Norbert Wiener, who worked on stochastic processes, and Eberhard Hopf, who worked on partial differential equations. The Wiener–Hopf technique combines two powerful

ideas: the Fourier transform and complex analysis. The Wiener–Hopf method has enabled us to analytically solve previously intractable integral and partial differential equations. To date, it remains the only known method for solving a wide class of physical problems. There are a numerous new directions of approximate methods which allow to tackle previously unapproachable real life problems.

The aim of this workshop is to share

(i) new tools for the solution of matrix Wiener-Hopf equation

(ii) the generalisations of the Wiener-Hopf method

(iii) the diverse applications of the Wiener-Hopf technique"

Timetable

Monday 12th August 2019
09:20 to 09:50	Registration	No Room Required
09:50 to 10:00	Welcome from David Abrahams (Isaac Newton Institute)	No Room Required
10:00 to 11:00	Frank Speck Universidade de Lisboa Wiener-Hopf factorisation through an intermediate space and applications to diffraction theory	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Eugene Shargorodsky King's College London Quantitative results on continuity of the spectral factorisation mapping	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:00	Raphael Assier University of Manchester Recent advances in the quarter-plane problem using functions of two complex variables	Room 1
14:00 to 14:30	J.M.L. Bernard ENS de Cachan Novel exact and asymptotic series with error functions, for a function involved in diffraction theory: the incomplete Bessel function	Room 1
14:30 to 15:00	Andrey Shanin Moscow State University Ordered Exponential (OE) equation as an alternative to the Wiener-Hopf method	Room 1
15:00 to 15:30	Anastasia Kisil University of Cambridge Generalisation of the Wiener-Hopf pole removal method and application to n by n matrix functions	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Basant Lal Sharma Wiener-Hopf factorisation on the unit circle: some examples of discrete scattering problems	Room 1
16:30 to 17:00	Grigori Giorgadze Tbilisi State University; Georgian Technical University On the partial indices of piecewise constant matrix functions	Room 1
17:00 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 13th August 2019
09:00 to 10:00	Ilya Spitkovsky New York University; College of William and Mary Wiener-Hopf factorization: the peculiarities of the matrix almost periodic case	Room 1
10:00 to 11:00	Lasha Ephremidze Tbilisi State University; New York University On Janashia-Lagvilava method of matrix spectral factorisation	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:30	Andreas Kyprianou University of Bath Wiener-Hopf Factorisations for Levy processes	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:30	Sergei Rogosin Belarusian State University Factorisation of triangular matrix-functions of arbitrary order	Room 1
14:30 to 15:00	Cristina Camara A Riemann-Hilbert approach to Einstein field equations	Room 1
15:00 to 15:30	Aloknath Chakrabarti Indian Institute of Science Solving Wiener-Hopf Problems by the aid of Fredholm Integral Equations of the Second Kind	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Victor Adukov South Ural State University On explicit and exact solutions of the Wiener-Hopf factorization problem for some matrix functions	Room 1
16:30 to 17:00	Valery Smyshlyaev University College London Whispering gallery waves diffraction by boundary inflection: an unsolved canonical problem	Room 1

Wednesday 14th August 2019
09:00 to 10:00	Michael Marder Analytical solutions of dynamic fracture and friction at the atomic scale	Room 1
10:00 to 10:30	John Raymond Willis University of Cambridge Transmission and reflection at an interface between metamaterial and ordinary material	Room 1
10:30 to 11:00	Leonid Slepyan Tel Aviv University Greater generality brings simplicity	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Alexander Movchan University of Liverpool Homogenisation and a Wiener-Hopf formulation for a scattering problem around a semi-infinite elastic structured duct	Room 1
12:00 to 12:30	Lev Truskinovsky ESPCI ParisTech Supersonic kinks in active solids	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 18:30	Free afternoon	No Room Required
19:30 to 22:00	Formal Dinner at Christ's College	No Room Required

Thursday 15th August 2019
09:00 to 10:00	Malte Peter Universität Augsburg Water-wave forcing on submerged plates	Room 1
10:00 to 10:30	Xun Huang Peking University; Hong Kong University of Science and Technology Turbofan noise detection and control studies by the Wiener-Hopf Technique	Room 1
10:30 to 11:00	Elena Luca University of California, San Diego Numerical solution of matrix Wiener–Hopf problems via a Riemann–Hilbert formulation	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Vito Daniele Politecnico di Torino Fredholm factorization of Wiener-Hopf equations (presented by Guido Lombardi)	Room 1
12:00 to 12:30	Guido Lombardi Politecnico di Torino Complex scattering and radiation problems using the Generalized Wiener-Hopf Technique	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:00	Justin Jaworski Lehigh University Owl-inspired mechanisms of turbulence noise reduction	Room 1
14:00 to 14:30	Nikolai Gorbushin ESPCI ParisTech Steady-state interfacial cracks in bi-material elastic lattices	Room 1
14:30 to 15:00	Matthew Priddin University of Cambridge Using iteration to solve n by n matrix Wiener-Hopf equations involving exponential factors with numerical implementation	Room 1
15:00 to 15:30	Francesco Dal corso University of Trento Moving boundary value problems in the dynamics of structures	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Larissa Fradkin Sound Mathematics Ltd Elastic wedge diffraction, with applications to non-destructive evaluation	Room 1
16:30 to 17:00	Davide Bigoni University of Trento Shear band dynamics	Room 1

Friday 16th August 2019
09:00 to 10:00	Dmitry Ponomarev Vienna University of Technology; Steklov Mathematical Institute, Russian Academy of Sciences Spectral theory of convolution operators on finite intervals: small and large interval asymptotics	Room 1
10:00 to 10:30	Michael Nieves Keele University; University of Cagliari Phase transition processes in flexural structured systems with rotational inertia	Room 1
10:30 to 11:00	Konstantin Ustinov Institute for Problems in Mechanics of Russian Academy of Sciences Application of Khrapkov’s technique of 2x2 matrix factorization to solving problems related to interface cracks	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Ian Thompson University of Liverpool Diffraction in Mindlin plates	Room 1
12:00 to 12:30	Pavlos Livasov Aberystwyth University Two vector Wiener-Hopf equations with 2x2 kernels containing oscillatory terms	Room 1
12:30 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:00	Alexander Galybin Russian Academy of Sciences Application of the Wiener-Hopf approach to incorrectly posed BVP of plane elasticity	Room 1
14:00 to 14:30	Matthew Colbrook University of Cambridge Solving Wiener-Hopf type problems numerically: a spectral method approach	Room 1
14:30 to 15:00	Ivan Argatov Malmö University Application of the Wiener–Hopf technique in contact problems	Room 1
15:00 to 15:30	Mikhail Lyalinov Saint Petersburg State University Functional-integral equations and diffraction by a truncated wedge	Room 1
15:30 to 16:00	Gennady Mishuris Aberystwyth University Comments on the approximate factorisation of matrix functions with unstable sets of partial indices	Room 1

Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications

Factorisation of matrix functions: New techniques and applications

Organisers

Guido Lombardi Politecnico di Torino
Gennady Mishuris Aberystwyth University

Participants

David Abrahams Isaac Newton Institute
Victor Adukov South Ural State University
Nataliia Adukova South Ural State University
Ivan Argatov Malmö University
Raphael Assier University of Manchester
Peter Baddoo University of Cambridge
David Baker University of Cambridge
Igor Berinskii Tel Aviv University
J.M.L. Bernard ENS de Cachan
Davide Bigoni University of Trento
Cristina Camara
Aloknath Chakrabarti Indian Institute of Science
John Chapman Keele University
Matthew Colbrook University of Cambridge
Francesco Dal corso University of Trento
Marina Dubatovskaya Belarusian State University
Lasha Ephremidze Tbilisi State University; New York University
Larissa Fradkin Sound Mathematics Ltd
Alexander Galybin Russian Academy of Sciences
Grigori Giorgadze Tbilisi State University; Georgian Technical University
Nikolai Gorbushin ESPCI ParisTech
Tony Hill King's College London
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
Michael Marder
Mike Meylan University of Newcastle, Australia
Gennady Mishuris Aberystwyth University
Alexander Movchan University of Liverpool
Natasha Movchan University of Liverpool
Matthew Nethercote University of Manchester
Michael Nieves Keele University; University of Cagliari
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
Ludmila Prikazchikova Keele University
Sergei Rogosin Belarusian State University
Andrey Shanin Moscow State University
Eugene Shargorodsky King's College London
Basant Lal Sharma
Leonid Slepyan Tel Aviv University
Valery Smyshlyaev University College London
Frank Speck Universidade de Lisboa
Ilya Spitkovsky New York University; College of William and Mary
Ian Thompson University of Liverpool
Lev Truskinovsky ESPCI ParisTech
Konstantin Ustinov Institute for Problems in Mechanics of Russian Academy of Sciences
Jiaqi Wang Shanghai Jiao Tong University
John Raymond Willis University of Cambridge
Peter Wootton Keele University

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Factorisation of matrix functions: New techniques and applications

Workshop theme

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