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Applied Asymptotics and Modelling

Edinburgh, 26-30 June 2006


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Scientific Programme and Participants

The Workshop starts with Registration (between 09.00 and 09.50) followed by talks on Monday 26 June and finishes in the afternoon of Friday 30 June. For programme click here, for participants here.

The purpose of the meeting is two-fold.
  • First we aim to bring together experts in the field to discuss the latest developments with a wider audience of interested mathematicians
  • .
  • Secondly, the meeting will also consider emerging areas of interdisciplinary science to which asymptotics may constructively contribute. They will be aided by survey talks from non- mathematicians, who will outline challenging and relevant questions, which will provide points of discussion for further work.
To facilitate these aims we shall hold sessions illustrating the development and applications of asymptotics in the following areas:
  • Multi-scale models, including biological models and nanotechnology;
  • Stochastic systems;
  • Deterministic models;
  • Dynamical systems and integrability;
  • Riemann-Hilbert problems and random matrix theory;
  • Recent advances in asymptotic theory.
The themes will consist of survey talks, research presentations and discussions.

Programme

Monday 26 June
09.00 - 09.50 Registration and coffee
09.50 - 10.00 Welcome
10.00 - 10.45 Ovidiu Costin (Ohio State University)
Borel summability in PDEs and applications to the time dependent Schrödinger equation
10.45 - 11.00 Coffee
11.00 - 11.45 Saleh Tanveer (Ohio State University)
Exponential asymptotics and singularities of PDEs
11.45 - 12.15 Rodica Costin (Ohio State University)
Results on the classification of nonlinear ODEs with several regular singular points
12.15 - 14.00 Lunch in Exhibition Room, ICMS
14.00 - 14.45 Adri Olde Daalhuis (University of Edinburgh) and Chris Howls (University of Southampton)
The higher-order Stokes phenomenon in nonlinear PDEs
14.45 - 15.30 Eric Delabaere (Université d'Angers)
Effective resummation and resurgence theory
15.30 - 16.15 Coffee/Tea and discussion on applications of asymptotics beyond all orders to PDEs
16.15 - 17.00 Takashi Aoki (Kinki University)
Sum relations for multiple zeta values and the Gauss hypergeometric function
17.00 - 17.45 André Voros (CEA/Service de Physique Théorique de Saclay)
Asymptotic sharpenings of Li's criterion for the Riemann Hypothesis
17.45 Wine Reception in Exhibition Room, ICMS
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Tuesday 27 June
09.00 - 09.45 Jonathan Sherratt (Heriot-Watt University)
An asymptotics problem from spatiotemporal population cycles
09.45 - 10.30 Sergei Kuksin (Heriot-Watt University)
Asymptotical problems in 2D turbulence
10.30 - 11.00 Coffee and discussion on application of asymptotics to stochastic systems
11.00 - 11.45 Stephen Cowley (University of Cambridge)
The exponentially small generation of turbulence
11.45 - 12.15 Elinborg Olafsdottir (University of Edinburgh)
Radiation of exponentially small inertia-gravity waves by a vortex
12.15 - 14.00 Lunch break
14.00 - 14.45 John King (University of Nottingham)
Asymptotic analysis of a simple model for cellular aggregation
14.45 - 15.30 Mark Chaplain (University of Dundee)
Asymptotic problems arising from the mathematical modelling of solid tumour growth
15.30 - 16.15 Coffee/Tea and discussion on applications of asymptotics to multi-scale biological systems
16.15 - 17.00 Robert O’Malley (University of Washington)
New and old ways of thinking about boundary layer resonance
17.00 - 17.45 Jacques Vanneste (University of Edinburgh)
Passive-scalar decay in fast flows
19.30 Informal meal at Nargile, Turkish Restaurant, 73 Hanover Street
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Wednesday 28 June
09.00 - 09.45 Arno Kuijlaars (Katholieke Universiteit Leuven)
Riemann Hilbert methods in random matrix theory
09.45 - 10.30 Alexander Its (Indiana University/Purdue University Indianapolis)
On the asymptotic analysis of Toeplitz determinants via the Riemann-Hilbert method
10.30 - 11.00 Coffee
11.00 - 11.45 Roderick Wong (City University of Hong Kong)
Global asymptotics and Riemann-Hilbert problems
11.45 - 12.15 Discussion on applications of the Riemann-Hilbert method in asymptotics
12.15 - 13.00 Nico Temme (Centrum voor Wiskunde en Informatica)
Exact solution approach of model problems in singular perturbations
13.00 onwards Lunch break and free afternoon. (ICMS open for discussion until 18.00)
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Thursday 29 June
09.00 - 09.45 John Billingham (University of Nottingham)
Kuzmak's method for slender, surface tension driven flows
09.45 - 10.30 Stephen Wilson (University of Strathclyde)
Asymptotic analysis of thin-film flows
10.30 - 11.00 Coffee and discussion on asymptotic applications to turbulence
11.00 - 11.45 Patrick Dorey (Durham University)
Differential equations and integrable models
11.45 - 12.30 Carl M Bender (Washington University, St Louis)
Using functional integration to establish the connection between PT-symmetric and Hermitian Hamiltonians
12.30 - 14.15 Lunch break
14.15 - 15.00 Jeremy Baumberg (University of Southampton)
To be confirmed
15.00 - 15.45 Jon Chapman (University of Oxford)
Asymptotics in dislocation modelling
15.45 - 16.15 Stephen J Watson (University of Glasgow/Northwestern University)
Singular limits via the principle of maximal dissipation
16.15 - 17.00 Tea and discussion of asymptotics to nanoscale systems
17.00 - 17.45 Alexander Movchan (University of Liverpool)
Asymptotic approximations of Green’s functions in singularly perturbed domains
17.45 - 19.00 Discussion of various open problems
19.30 Workshop Dinner at First Coast Restaurant, 99-101 Dalry Road
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Friday 30 June
09.00 - 09.45 Vassili Gelfreich (University of Warwick)
Stokes phenomenon near a parabolic fixed point of an analytic map in C^2
09.45 - 10.30 Claude Baesens (University of Warwick)
Exponentially good aproximation of incommensurate structures by arrays of discommensurations in Frenkel-Kontorova
10.30 - 11.00 Coffee and discussion on applications of exponential asymptotics to dynamical systems
11.00- 11.45 Peter Clarkson (University of Kent)
Asymptotics and connection formulae for Painlevé equations
11.45 - 12.15 Tatsuya Koike (Kyoto University)
On the exact WKB analysis of simple pole type operators
12.15 - 14.00 Lunch break
14.00 - 14.45 Yoshitsugu Takei (Kyoto University)
Toward the exact WKB analysis for instanton-type solutions for Painlevé hierarchies
14.45 - 15.30 Richard B Paris (University of Abertay)
Exactification of the method of steepest descents
15.30 - 16.00 Coffee/Tea
16.00 - 16.45 José L López (Public University of Navarra)
Asymptotic methods for Mellin convolution integrals demystified
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Expected Particpants

The following have indicated their willingness to participate:

Name Institution
Aoki, Takashi Kinki University
Baesens, Claude University of Warwick
Baumberg, Jeremy University of Southampton
Bender, Carl M Washington University, St Louis
Billingham, John University of Nottingham
Byatt-Smith, John University of Edinburgh
Chaplain, Mark University of Dundee
Chapman, Jon University of Oxford
Clarkson, Peter University of Kent
Costin, Ovidiu Ohio State University
Costin, Rodica D Ohio State University
Cowley, Stephen University of Cambridge
Dai, Dan City University of Hong Kong
Delabaere, Eric Université d'Angers
Dorey, Patrick Durham University
Ferreira, Chelo Universidad de Zaragoza
Gelfreich, Vassili University of Warwick
Howls, Chris University of Southampton
Its, Alexander Indiana University/Purdue University Indianapolis
King, John University of Nottingham
Koike, Tatsuya Kyoto University
Kuijlaars, Arno Katholieke Universiteit Leuven
Kuksin, Sergei Heriot-Watt University
López, José L Public University of Navarra
Movchan, Alexander University of Liverpool
Olafsdottir, Elinborg University of Edinburgh
Olde Daalhuis, Adri University of Edinburgh
O'Malley, Robert University of Washington
Pagola, Pedro Universidad Pública de Navarra
Paris, Richard B University of Abertay
Parker, David University of Edinburgh
Pérez-Sinusía, Ester Universidad Nacional de Educación a Distancia
Sherratt, Jonathan Heriot-Watt University
Takei, Yoshitsugu Kyoto University
Tanveer, Saleh Ohio State University
Temme, Nico Centrum voor Wiskunde en Informatica (CWI)
Vanneste, Jacques University of Edinburgh
Voros, André CEA/Service de Physique Théorique de Saclay
Watson, Stephen University of Glasgow/Northwestern University
Wilson, Stephen University of Strathclyde
Wong, Roderick City University of Hong Kong
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