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Topology of moduli spaces of vector bundles on a real algebraic curve

Presented by: 
FMR Schaffhauser [Los Andes]
Date: 
Tuesday 28th June 2011 - 14:40 to 15:10
Venue: 
INI Seminar Room 1
Abstract: 
Moduli spaces of real and quaternionic vector bundles on a curve can be expressed as Lagrangian quotients and embedded into the symplectic quotient corresponding to the moduli variety of holomorphic vector bundles of fixed rank and degree on a smooth complex projective curve. From the algebraic point of view, these Lagrangian quotients are irreducible sets of real points inside a complex moduli variety endowed with an anti-holomorphic involution. This presentation as a quotient enables us to generalise the equivariant methods of Atiyah and Bott to a setting with involutions, and compute the mod 2 Poincaré series of these real algebraic varieties. This is joint work with Chiu-Chu Melissa Liu (Columbia).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons