### Higgs bundles and Hermitian symmetric spaces

Rubio, R *(Oxford)*

Monday 27 June 2011, 14:40-15:10

Seminar Room 1, Newton Institute

#### Abstract

We study the moduli space of polystable G-Higgs bundles for noncompact real Lie groups G of Hermitian type. First, we define the Toledo character and use it to define the Toledo invariant, for which a Milnor-Wood type inequality is proved. Then, for the maximal value of the Toledo invariant, we state a Cayley correspondence for groups of so-called tube type and point out a rigidity theorem for groups of so-called non-tube type. The proofs of these results are based on the Jordan algebra structure related to the tangent space of the Hermitian symmetric space given by G and are independent of the classification theorem of Lie groups. (Joint work with O. Biquard and Ó. García-Prada.)

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