The geometry and cohomology of moduli spaces of vector bundles
Moduli spaces are geometric solutions to classification problems in algebraic geometry. One of the most classical examples is the moduli of vector bundles on a Riemann surface, which has very rich geometry and has connections with representation theory and mathematical physics. I will describe the geometry of these moduli spaces and survey some results on their various cohomological invariants. Finally I will present some joint work with Simon Pepin Lehalleur on the motives of these moduli spaces, which unify different cohomological invariants and also encode Chow groups describing subvarieties of these moduli spaces.
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