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Algebraic Geometry Seminar

Monday, April 18, 2016
4:00pm to 5:00pm
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Quantum representations and higher-rank Prym varieties
Johan Martens, Lecturer and Chancellor Fellow, Mathematics, University of Edinburgh,

Riemann's moduli space of curves can naturally be equipped with a range 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, who 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 the projective representations of the mapping class group they give rise to.

For a few sporadic, low-level versions this difference brakes down though, 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 ongoing work with T. Baier, M. Bolognesi and C. Pauly.

For more information, please contact Mathematics Department by email at [email protected] or visit http://www.its.caltech.edu/~pablos/seminars.html.