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
invo- lution. 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.