Warwick EPSRC Symposium in the Statistical Mechanics / Mathematics of Phase Transitions

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This is a proposal for a symposium to be held during the academic year 2013-2014 at the Mathematics Research Centre (MRC) of the University of Warwick. The overall theme is mathematical statistical physics with a particular emphasis on the extension of its methods to a range of disciplines within mathematics as well as its applications in physics and other sciences. Mathematical statistical mechanics developed from its focus on rigorous foundations of statistical physics to become an exciting and active area of research devoted to various aspects of collective phenomena. Remarkably, its methods designed originally for exploring phase transitions are providing effective tools in other branches of mathematics: combinatorics, discrete mathematics, probability, analysis, and computer science. They turned out to be especially useful for investigations of asymptotics with abrupt thresholds and universal behaviour at criticality, the topics brought together under the heading "Mathematics of Phase Transitions". This is exemplified by impressive successes in various disciplines. a) In probability: studies of universal critical behaviour of various two-dimensional systems based on Schramm's SLE led to spectacular advances and opened a whole new field of modern mathematics with Fields Medals awarded in 2006 and 2010. b) In discrete mathematics and computer science: the theory of random discrete structures that is crucial for these disciplines has been truly revolutionised by new ideas from statistical mechanics. c) In analysis: investigations of macroscopic nonlinear PDE, as applied, for example, in nonlinear elasticity or in investigations of phase coexistence, based on underlying microscopic atomic models are gaining prominence.The symposium will facilitate a year-long sustained research activity on mathematical aspects of statistical physics with emphasis on its links to other mathematical disciplines. It will foster international links and collaborations and attract the attention of the UK mathematical community to this newly emerging and highly active area and enable the innovative use of the potential of branches of mathematics that are well established in the UK.In practical terms the symposium will be structured around six week-long workshops in various research areas of international significance pertaining to the general theme of the symposium. All important areas of mathematics where the methods of statistical physics play a significant role will be covered, with participation of leading international and national experts.In addition, there will be a visitor programme and a number of other supporting activities (mini-courses, seminars) designed to sustain the level of activity through the year.