Tamas Hausel
Published 2011-02-08, updated 2011-09-10Version 2
Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory.
Comments: 41 pages, small changes and clarifications, to appear in Handbook of Moduli
Algebraic cycles and Hitchin systems
Finite groups of symplectic automorphisms of hyperkähler manifolds of type $K3^{[2]}$
Finite Groups of Essential Dimension 2
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