Entrance hall of the ICMS Workshop

Applied and computational complex analysis

May 08, 2017 - May 12, 2017

ICMS, 15 South College Street, Edinburgh, EH8 9AA

Organisers

Name Institution
Clarkson, Peter University of Kent
Crowdy, Darren Imperial College London
Fokas, Thanasis University of Cambridge
McDonald, Robb University College London
Pelloni, Beatrice Heriot-Watt University

 Bringing together mathematicians, at all career stages, who share an interest in using fundamental complex analysis methods  this workshop will explore new and deep mathematical connections between shapes, transforms, spectral analysis and inverse problems. The programme is deliberately wide in scope with participants having research interests covering aspects of the theoretical development of complex analysis, associated computational methods and application to problems of medical, industrial and geophysical importance.The following challenges will be addressed at the workshop:

• Shape evolution in interface dynamics.
• Shape emergence in the Painlevé equations.
• Special function theory and asymptotics.
• Spectral analysis, transforms and medical imaging.

The organisers expect that the workshop will: allow for an  an exchange of the latest  developments and results of researchers covering a wide range of applied and computational complex analysis and, consequently, raising of the awareness of the power of these approaches to the next generation of applied mathematicians;  that outstanding problems will be identified, both theoretical and applied, which can be tackled using complex analysis and associated numerical methods; and importantly that there will be the initiation of collaborations, especially between researchers working in different areas of applied and computational complex analysis. Ultimately, it is anticipated that the mathematical techniques discussed and developed as a result of the workshop should eventually become widely used in industrial, biological and physical applications.

Group photographs available from our Flickr account.

Arrangements

This workshop will commence with Registration at 09.00 on Monday morning 8 May 2017 and close at 13.00 on Friday 12 May 2017. 

 

Participation
Participation for this workshop will be by invitation only.   Invitations were issued in January 2017. 

 

Registration fee
A registration fee of 100.00 GBP is payable by all participants (excluding Organisers).  Payment can be made on arrival at ICMS - at Registration we will accept cash, credit/debit card payments and sterling cheques (payable to “Heriot-Watt University”).  Unfortunately, we do not yet have an on-line payment system at ICMS.   If you wish to pay by credit/debit card, please complete this credit/debit card form and bring the completed form to Registration.   

 

Venue
The workshop will be held at ICMS, 15 South College Street, Edinburgh, EH8 9AA. You may also find this map useful for the workshop.

 

Talks
Talks will be allocated 40 minutes (which includes 5-10 minutes of questions/answers).  Talks will be held in the Newhaven Lecture Theatre.  The Lecture Theatre is equipped with a data projector, computer, visualiser (the new generation of overhead projectors) and two blackboards.  The projector and one board may be used simultaneously.  It is best to bring your presentation on a memory stick to use in our ICMS computer.  Alternatively, it is possible for you to use your own laptop with our dataprojector, but please be aware that you may have to alter your laptop resolutions/settings.  

 

Public Lecture
On Wednesdy10 May, Peter Clarkson (University of Kent) will give a Public Lecture.  Doors will open to the public at 17.30, with the lecture starting at 18.00.   The lecture will be followed by an informal wine reception in the Chapterhouse on Level 1.   Seats have been reserved for the workshop participants, so no action is needed to attend.

  • Rogue waves, tsunamis and solitons
    In 1834, John Scott Russell, a Scottish engineer, naval architect and shipbuilder, first observed a solitary wave whilst riding on horseback beside the narrow Union canal near Edinburgh. Scott Russell did extensive experiments in a laboratory scale wave tank in order to study the phenomenon he had observed. Subsequently, in the nineteenth century French, English and Dutch scientists undertook studies related to the solitary wave observed by Scott Russell. 

    It was not until the 1960's when scientists began to use modern computers, that Russell's ideas began to be fully appreciated. In 1965, Zabusky and Kruskal's numerical calculations led them to call these solitary waves "solitons". Subsequently it has been discovered that solitons arise in numerous applications such as water waves and fibre optics. Phenomena such as rogue waves (also known as freak waves), which are large unexpected, suddenly appearing waves that can be extremely dangerous, and tsunamis are related to solitons.

    In this talk, I shall describe some of the history of the soliton and illustrate some of the applications.

 

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. 

 

Travel
Information about travel to the UK and Edinburgh is available here.

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies (volcanic ash disruptions) that may occur on your trip.

A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a one-way journey.     There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return - the Airlink 100.  This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the accommodation and the workshop venue (see map in 'Venue' section above). 

Lothian buses charge £1.60 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.

If travelling by train, please note that Edinburgh has several railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street.  If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge. The second large railway station is called Haymarket and is at the West End of the city centre.    Please be aware that there is also an Edinburgh Park railway station but this is at the west side of the city some way from the city centre.  For ICMS, use Edinburgh Waverley.

 

Catering
Lunch will be served in the Chapterhouse on Level 1 at ICMS on Monday, Tuesday, Wednesday and Thursday.   Please note that no lunch is provided on Friday as the workshop closes at 13.00.   Refreshments will be provided in the coffee breaks for the duration of the workshop.   There will be an informal wine reception on Monday evening in the Chapterhouse, and again on Wednesday evening following the Public Lecture.   The workshop dinner will be on Thursday 11 May, 19.00, at Blonde Restaurant, 75 St Leonard's Street, Edinburgh.    

 

Programme

 Please continue to check this Programme until the time of the workshop as any alterations will be notified here.

You may download the abstracts for the workshop here

 Monday 8 May

09.00-09.50

Registration

09.50-10.00

Opening remarks

10.00-10.40

Stefan Llewellyn Smith (University of California, San Diego)
Solving matrix Wiener-Hopf problems numerically via Riemann-Hilbert problems
pdf of presentation

10.40-11.20

Anastasia Kisil (University of Cambridge)
Approximate matrix Wiener-Hopf factorisations and applications to problems in acoustics

11.20-11.50

Coffee/tea served in the Chapterhouse

11.50-12.30

Alex Himonas (University of Notre Dame)
The unified transform method amd well-posedness of nonlinear dispersive equations

12.30-13.40

Lunch served in the Chapterhouse

13.40-14.20

Natalie Sheils (University of Minnesota/Institute for Math and Its Applications)
The heat equation with imperfect thermal contact in a composite medium
pdf of presentation

14.20-15.00

Elena Louca (University of California, San Diego)
A new transform approach to biharmonic boundary value problems in polygonal and circular domains
pdf of presentation

15.00-15.30

Coffee/tea in the Chapterhouse

15.30-16.10

Rhodri Nelson (Imperial College London)
Outer boundary effects in a petroleum reservoir

16.10-16.50

Kostas Kalimeris (RICAM, Austria)
A non-local formulation for two-dimensional water waves

16.50-17.20

Day 1 wrap-up and discussion (Thanasis Fokas)

17.20-19.00

Wine reception

 

Tuesday 9 May

09.20-10.00

Rod Halburd (University College London)
Integrable delay-differential equations

10.00-10.40

Ana Loureiro (University of Kent)
On star-symmetric polynomials with classical behaviour

10.40-11.10

Coffee/tea

11.10-11.50

Claire Gilson (University of Glasgow)
Constructing and deconstructing solutions in ultra discrete integrable systems

11.50-12.30

Sara Lombardo (Nothumbria University)
Linear stability analysis of integrable partial differential equations

12.30-13.40

Lunch

13.40-14.20

Elizabeth Mansfield (University of Kent)
Discrete moving frames and discrete variational problems

14.20-15.00

Adri Olde Daalhuis (University of Edinburgh)
Computation of the coefficients appearing in the uniform asymptotic expansions of integrals

15.00-15.30

Coffee/tea

15.30-16.10

Alfredo Deaño (University of Kent)
Special function solutions of Painleve II and Painleve IV: asymptotic and numerical study

16.10-16.50

David Gómez-Ullate Oteiza (ICMAT and Universidad Complutense Madrid)
Durfee rectangles, exceptional Hermite polynomials and rational solutions to Painleve equations

16.50-17.20

Day 2 wrap up and discussion (Peter Clarkson)

 

Wednesday 10 May

9.20-10.00

Peter Olver (University of Minnesota)
Dispersive quantization of linear and nonlinear waves

10.00-10.40

Olga Trichtchenko (ICERM, Brown University)
Solutions and stability for fexural-gravity waves

10.40-11.10

Coffee/tea

11.10-11.50

Mark Mineev-Weinstein (UFPE)
Thermodynamics of the Laplacian Growth

11.50-12.30

Tamara Grava (SISSA)
Universality of critical behaviour in Hamiltonian PDEs

12.30-13.40

Lunch served

13.40-14.20

Chris Howls (University of Southampton)
Invisible catastrophes: when to turn an asymptotic blind eye

14.20-15.00

Day 3 wrap-up and discussion (Darren Crowdy)

15.00-15.20

Coffee/tea

 

 

17.30-18.00

Doors open to the public

18.00-19.00

Public Lecture by Peter Clarkson (University of Kent)
Rogue waves, tsunamis and solitons

19.00-20.00

Public lecture wine reception

 

 Thursday 11 May

09.20-10.00

Linda Cummings (New Jersey Institute of Technology)
Slow viscous flows in doubly connected domains

10.00-10.40

Folkmar Bornemann(Technische Universität München)
Numerical problems inspired by discrete complex analysis

10.40-11.10

Coffee/tea

11.10-11.50

Anthony Davis (University of California, San Diego)
Non existence of further closed form 2-D sloshing modes in a symmetric triangular basin
pdf of presentation

11.50-12.30

Gergő Nemes (University of Edinburgh)
Computable error bounds for asymptotic expansions of integrals via resurgence

12.30-13.40

Lunch served

13.40-14.20

David Smith (Yale-NUS College, Singapore)
Nonlocal problems for linear evolution equations

14.20-15.00

John King (University of Nottingham)
Complex-plane analysis of diffusive travelling waves

15.00-15.30

Coffee/tea

15.30-16.10

Michael Dallaston (Imperial College London)
Asymptotic selection of self-similar rupture solutions to a generalised thin film equation

16.10-16.50

Iasonas Hitzazis (Imperial College London)
Linear elliptic PDEs in a cylindrical domain with a polygonal cross-section

16.50-17.20

Day 4 wrap-up and discussion (Beatrice Pelloni)

 

 

19.00

Workshop dinner at Blonde

 

 Friday 12 May

10.00-10.40

Bartosz Protas (McMaster University)
On the stability of free-boundary problems: a case study in vortex dynamics
pdf of presentation

10.40-11.10

Coffee/tea

11.10-11.50

Mark Blyth (University of East Anglia)
Deformation of an elastic cell under inviscid flow

11.50-12.30

Edward Johnson (University College London)
Rotating vortical outflows

12.30 -13.00

Day 5 wrap-up, discussion and close (Robb McDonald)

 

You may download the abstracts for the workshop here

Presentations:

Presentation Details
Abrahams, I David
Corner singularities and improved convergence of eigenfunction expansions in acoustics, electromagnetics and elasticity
View Abstract Down
Blyth, Mark
Deformation of an elastic cell under inviscid flow
View Abstract Down
Bornemann, Folkmar
Numerical problems inspired by discrete complex analysis
View Abstract Down
Cummings, Linda
Slow viscous flows in doubly-connected domains
View Abstract Down
Dallaston, Michael
Asymptotic selection of self-similar rupture solutions to a generalised thin film equation
View Abstract Down
Davis, Anthony
Non existence of further closed form 2-D sloshing modes in a symmetric triangular basin
View Abstract Down
Deaño, Alfredo
Special function solutions of Painlevé II and IV: asymptotic and numerical study
View Abstract Down
Gilson, Claire
Constructing and deconstructing solutions in ultra discrete integrable systems
View Abstract Down
Gómez-Ullate Oteiza, David
Durfee rectangles, exceptional Hermite polynomials and rational solutions to Painlevé equations
View Abstract Down
Grava, Tamara
Universality of critical behaviour in Hamiltonian PDEs
View Abstract Down
Halburd, Rod
Integrable delay-differential equations
View Abstract Down
Himonas, Alex
The unified transform method and well-posedness of nonlinear dispersive equations
View Abstract Down
Hitzazis, Iasonas
Linear elliptic PDEs in a cylindrical domain with a polygonal cross-section
View Abstract Down
Howls, Chris
Invisible catastrophes: when to turn an asymptotic blind eye
View Abstract Down
Johnson, Edward
Rotating vortical outflows
View Abstract Down
Kalimeris, Kostas
A non-local formulation for two-dimensional water waves
View Abstract Down
King, John
Complex-plane analysis of diffusive travelling waves
View Abstract Down
Kisil, Anastasia
Approximate matrix Wiener-Hopf factorisations and applications to problems in acoustics
View Abstract Down
Llewellyn Smith, Stefan
Solving matrix Wiener-Hopf problems numerically via Riemann-Hilbert problems
View Abstract Down
Lombardo, Sara
Linear stability analysis of integrable partial differential equations
View Abstract Down
Louca, Elena
A new transform approach to biharmonic boundary value problems in polygonal and circular domains
View Abstract Down
Loureiro, Ana
On star-symmetric polynomials with a classical behaviour
View Abstract Down
Mansfield, Elizabeth
Discrete moving frames and discrete variational problems
View Abstract Down
Mineev-Weinstein, Mark
Thermodynamics of the Laplacian growth
View Abstract Down
Nelson, Rhodri
Outer boundary effects in a petroleum reservoir
View Abstract Down
Nemes, Gergő
Computable error bounds for asymptotic expansions of integrals via resurgence
View Abstract Down
Olde Daalhuis, Adri
Computation of the coefficients appearing in the uniform asymptotic expansions of integrals
View Abstract Down
Olver, Peter
Dispersive quantization of linear and nonlinear waves
View Abstract Down
Protas, Bartosz
On the stability of free-boundary problems: a case study in vortex dynamics
View Abstract Down
Sheils, Natalie
The heat equation with imperfect thermal contact in a composite medium
View Abstract Down
Smith, David
Nonlocal problems for linear evolution equations
View Abstract Down
Trichtchenko, Olga
Solutions and stability for flexural-gravity waves
View Abstract Down

Participants

Name Institution
Blyth, Mark University of East Anglia
Bornemann, Folkmar Technische Universität München
Clarkson, Peter University of Kent
Clift, Richard Loughborough University
Crowdy, Darren Imperial College London
Cummings, Linda New Jersey Institute of Technology
Dallaston, Michael Imperial College London
Davis, Anthony University of California, San Diego
Deaño, Alfredo University of Kent
Fokas, Thanasis University of Cambridge
Gilson, Claire University of Glasgow
Gómez-Ullate Oteiza, David ICMAT & Universidad Complutense Madrid
Grava, Tamara SISSA
Halburd, Rod University College London
Himonas, Alex University of Notre Dame
Hitzazis, Iasonas University of Cambridge
Howison, Sam University of Oxford
Howls, Chris University of Southampton
Johnson, Edward University College London
Kalimeris, Kostas RICAM, Austria
King, John University of Nottingham
Kisil, Anastasia University of Cambridge
Lacey, Andrew Heriot-Watt University
Llewellyn Smith, Stefan University of California, San Diego
Lombardo, Sara Nothumbria University
Louca, Elena University of California, San Diego
Loureiro, Ana University of Kent
Mansfield, Elizabeth University of Kent
McDonald, Robb University College London
Mineev-Weinstein, Mark UFPE
Nelson, Rhodri Imperial College London
Nemes, Gergő University of Edinburgh
Olde Daalhuis, Adri University of Edinburgh
Olver, Peter University of Minnesota
Pelloni, Beatrice Heriot-Watt University
Protas, Bartosz McMaster University
Sheils, Natalie University of Minnesota/Institute for Math and Its Applications
Smith, David Yale-NUS College, Singapore
Trichtchenko, Olga ICERM, Brown University