[Om-announce] - Call for Applications - ESF-EMS/ERCOM/INI Conference: Highly Oscillatory Problems: From Theory to Applications, 12-17 September 2010, Cambridge, UK

Aurelie Sissler ASissler at esf.org
Mon Mar 22 14:43:50 CET 2010

- Call for Applications – Conference on Highly Oscillatory Problems: From Theory to Applications
The Isaac Newton Institute, Cambridge, UK
12-17 September 2010

Chair: Arieh Iserles, Cambridge University, UK

Co-chair: Claude Le Bris - ENPC, Champs-sur-Marne, FR

The recent six-months' programme on “Highly oscillatory problems: Computation, theory and applications” at the Isaac Newton Institute of Mathematical Sciences (January–July 2007) represented an important paradigm shift. Historically research into high oscillation had been scattered across many subject areas of pure and applied mathematics, with little cross-disciplinary communication and interaction. The INI programme rendered high oscillation into an organising principle for concerted inter-disciplinary research effort. An important purpose of the proposed conference is to follow up on the success of the INI programme and continue to foster the knowledge base of mathematical research into high oscillation across different disciplines and subject areas, with particular emphasis on computational issues. Cross disciplinarity of the proposed conference is not just a convenient optional extra, it is  in the very nature of the underlying subject matter. As the INI programme demonstrated, it is absolutely essential to bring together the different threads of high oscillation research, from mathematical theory, computation and the varied application areas, forge common terminology and learn from each other. It is equally important to maintain constant flow of ideas between mathematical experts and workers in the many application areas where high oscillation is such an important phenomenon.

Among the many issues we plan to address in the conference, we wish to single out the following:
1. Electromagnetic and acoustic scattering: Solving direct acoustic and electromagnetic problems is a key task in many engineering simulations (electronics and communication technology). It also plays crucial role in inverse problems (radar, sonar, ultrasound and seismic imaging) . The problem intrinsically involves high oscillations, while simplified asymptotic models often fail to deliver sufficient accuracy.
2. Wave mechanics: Wide range of problems is modelled by Schrödinger equations with large potentials, which exhibit rapid oscillation. The challenge here is to design practical algorithms that produce solutions, which are accurate while respecting structural  attributes of the equation, and are not degraded in the presence of rapid oscillation.
3. Multiscale problems: Many large-scale physical problems involve highly oscillatory solutions that exhibit many non-separable scales. A key mathematical difficulty is when a problem has no natural scale separation, so traditional asymptotic methods fail to yield  useful models. New systematic multiscale analysis needs to be developed that can account  for interaction of infinitely many non-separable scales. Another challenge is to combine stochastic and highly oscillatory phenomena in this setting.
4. Homogenisation: A major tool of multiscale analysis is homogenization theory, applicable  to nonlinear dynamic problems without scale separation. An enduring challenge is to  analyse mathematically a range of ad hoc upscaling models, e.g. for two-phase flows and to provide rigorous numerical justification.
5. Symplectic algorithms: Realistic Hamiltonian potentials, e.g. in celestial mechanics or molecular dynamics, lead to high oscillation. This presents an important challenge to geometric numerical integration of Hamiltonian problems across long time scales. Although important advances have been recently recorded, using backward error analysis and modulated Fourier expansions, much remains to be done.
6. Computational asymptotics: Recent important work on multivariate highly oscillatory integration has led to very effective and affordable computational algorithms for classes of such integrals. Asymptotics-based approaches have also paved the way for fast simulation of wave scattering at high frequencies. These algorithms are based on the combination of classical numerical analysis with asymptotic theory.
7. Riemann–Hilbert techniques: Such techniques came of age in the last decade and have  been applied to a wide range of problems, from random matrices to partial differential  equations and orthogonal polynomials. In the context of partial differential equations,  they offer exciting new techniques to deal with high oscillation by means of integral transforms.
8. Theory of highly oscillatory partial differential equations: Pure mathematics often acts as a hothouse for ideas and concepts that ultimately filter, through the agency of applied mathematics, into application areas. There are numerous examples of recent developments of this kind, with great potential to practical applications.

Conference format:
• lectures by invited high level speakers
• short talks by young & early stage researchers
• poster sessions, round table and open discussion periods
• forward look panel discussion about future developments

Invited speakers will include:
• Assyr Abdulle - EPFL Lausanne, CH
• Dario Bambusi - University of Milano, IT
• Oscar Bruno - University of Caltech, US
• Yalchin Efendiev - Texas A&M, US
• Thanasis Fokas - University of Cambridge, UK
• Irene Fonseca - Carnegie Mellon University (CMU), US
• Daan Huybrechs - Katholieke Universiteit Leuven (KUL), BE
• Caroline Lasser - Freie Universität Berlin, DE
• Tony Lelievre - CERMICS - ENPC, FR
• Christian Lubich - University of Tübingen, DE
• Peter Markowich - University of Cambridge, UK
• Houman Owhadi - University of Caltech, US
• Ilaria Perugia - University of Pavia, IT
• Chus Sanz-Serna - University of Valladolid, ES
• Andrew Stuart - University of Warwick, UK
• Isabelle Terrasse - Aerospatiale Paris, FR
• Edriss Titi - Weizmann, IL & UC Irvine, US
• Weinan E - University of Princeton, US

Full conference programme and application form accessible online from www.esf.org/conferences/10340

Applications received up until 2 April 2010 only will be considered for grants.
Deadline for all applications 12 June 2010.

ESF Contact: Alessandra Piccolotto - apiccolotto at esf.org

This conference is organised by the European Science Foundation (ESF), in partnership with the European Mathematical Society (EMS), the European Research Centres on Mathematics (ERCOM) and the Isaac Newton Institute (INI).
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