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Glassy Systems and Constrained Stochastic Dynamics

9th-11th June

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The aim of this three day workshop is to bring together mathematicians and physicists who are working on stochastic dynamics, to share new ideas and methods for studying glassy systems, with a view to establishing new research directions and collaborations.

A glass transition is described by a dynamical crossover through which a viscous liquid falls out of equilibrium and appears solid on relevant observable time scales. Kinetically constrained models (KCMs) are stochastic particle systems, evolving with a simple Glauber dynamics, in which updates are restricted by local kinetic constraints. KCMs have proven to be extremely good models for the dynamics of glassy and amorphous materials, and have recently been studied extensively using rigorous probabilistic and heuristic approaches. In spite of their simple definition, these models display many key dynamical features of real glassy materials, such as ergodicity breaking transitions, huge relaxation times at low temperature, super-Arrhenius behavior, dynamic heterogeneity (i.e. non-trivial spatio-temporal fluctuations of the local relaxation to equilibrium), ageing and metastability. These features significantly complicate reliable numerical investigations which are often dominated by finite-size effects, and a close collaboration between mathematics and theoretical physics is essential to gain a full understanding.