Riemann Surfaces and their Associated Moduli Spaces

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By the uniformisation theorem, an orientable surface with finite genus and finitely many marked points admits a conformal structure and thus it is a Riemann surface. The space of conformal structures form the moduli space of Riemann surfaces. These objects and spaces have been at the forefront of many of the modern developments in geometry, topology and dynamics. The course will survey the theory of Riemann surfaces and associated moduli spaces (for instance, of holomorphic quadratic differentials). The focus will be geometric/ topological initially and dynamical towards the end of the course.