Geometry Seminar

Riemann’s moduli space of curves can naturally be equipped with a collection of bundles, whose fibres are spaces of non-abelian theta functions or, equivalently, spaces of conformal blocks.  These bundles come naturally equipped with flat projective connections, in many ways mirroring an old story for (abelian) theta functions, which were classically known to satisfy a heat-equation.  In some aspects, however, the non-abelian theta functions behave quite differently, most clearly exhibited when considering their monodromy, which typically is infinite.  For a few sporadic, low-level versions this difference brakes down however, a phenomenon best understood through strange duality.  In this talk we will describe the situation for rank 4, where the situation gets clarified by thinking about higher-rank Prym varieties.  This is joint work with T. Baier, M. Bolognesi and C. Pauly.