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

**Schaffhauser, FMR ***(Los Andes)*

Tuesday 28 June 2011, 14:40-15:10

Seminar Room 1, Newton Institute

#### 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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