Higgs bundles are vector bundles equipped with an additional "twisted endomorphism". Introduced by Nigel Hitchin in a context of mathematical physics, they have turned to be central objects in differential and algebraic geometry. In particular, moduli spaces of Higgs bundles have a very rich geometry that is both related to the geometry of moduli of vector bundles but also has additional symplectic features. I will introduce these moduli spaces and discuss some of what is known about their cohomology and their motivic invariants. There has been a lot of recent progress in this direction and I will try to describe the main threads. I will conclude with a discussion of my joint work with Victoria Hoskins on a motivic version of the "cohomological mirror symmetry" conjecture of Hausel and Thaddeus for SL_n and PGL_n Higgs bundles.

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Meeting ID: 9086116889
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