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Theoretical Aspects of Pattern Formation

19th September 2005 to 23rd September 2005

Organisers: Ian Melbourne (Surrey), Alastair Rucklidge (Leeds), and Bjorn Sandstede (Surrey)

Supported by the Newton Institute, the London Mathematical Society, EPSRC and the Institute of Advanced Studies (U Surrey)

Workshop Theme

Pattern formation is a wide-ranging subject, encompassing areas from fluid mechanics to solid-state physics, and from chemical to biological systems. Pattern formation is also a rich source of mathematical problems, providing interesting mathematical challenges in the field of applied partial differential equations, nonlinear dynamics and bifurcation theory. The formation of patterns in small domains can be studied near onset by a bifurcation-theoretic approach, but the range of validity of the normal form equations shrinks to zero as the domain size increases. The resolution of this issue is to employ a continuum description of bifurcating patterns in unbounded domains. In one space dimension, the reduction to an amplitude equation has been put on a rigorous mathematical foundation. However, similar progress on two-dimensional pattern formation is prevented by a fundamental mathematical difficulty: the orientational degeneracy of the plane. This workshop is intended to address aspects of this problem, and will bring together leading pure and applied mathematicians and experimentalists to examine the issues common to a wide variety of pattern-forming problems when these are posed in domains that are large compared to the intrinsic characteristic length scales of the pattern.

IAS Seminar

There will be a special day of distinguished lectures during the workshop, on Tuesday 20 September, aimed towards describing the state of the art of the subject as well as future directions. The distinguished invited speakers will be Guenter Ahlers (UC Santa Barbara), Dwight Barkley (Warwick), Alan Newell (Arizona), Arnd Scheel (Minneapolis), Eugene Wayne (Boston). This special day is intended for a wider academic audience and will be funded by the Institute of Advanced Studies (U Surrey)

University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons