Dynamics of topological defects in active matter on curved manifolds

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Topological defects are known to play an important role in the statics and dynamics of matter in equilibrium. It is less clear how such defects modify the behaviour of matter out of equilibrium. This project will investigate the role played by topological defects in "active matter", a paradigm of non-equilibrium, confined to curved manifolds. The techniques used will include differential geometry, partial differential equations, stochastic processes, and numerical methods.