Olof Bergvall

Genus three is arguably the first genus where curves exhibit general behaviour and is therefore a natural and important testing ground for new ideas. In this talk I will explain how the classical theory of genus three curves, in particular plane quartics and their bitangents, relates to more modern concepts, such as level structures and spin, and how this allows us to compute the cohomology groups of certain moduli spaces of genus three curves with symplectic level two structure (as representations of the corresponding symplectic group) using tools from algebraic geometry, combinatorics, commutative algebra and number theory.