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.
- 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.
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 |
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 |
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) |
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 |
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 |
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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