Global topology of the Hitchin system

Abstract

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.

41 pages, small changes and clarifications, to appear in Handbook of Moduli

References in corpus (11)

• Le lemme fondamental pour les groupes unitaires
• On the E-polynomials of a family of Character Varieties
• Mirror Symmetry, Hitchin's Equations, And Langlands Duality
• Le lemme fondamental pour les algebres de Lie
• Yang-Mills theory and Tamagawa numbers
• Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs
• Topology of Hitchin systems and Hodge theory of character varieties: the case A_1
• Towards a Global Springer Theory III: Endoscopy and Langlands duality
• Towards a Global Springer Theory II: the double affine action
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Cited by in corpus (15)

• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Stratifications on the Moduli Space of Higgs Bundles
• Aspects of the topology and combinatorics of Higgs bundle moduli spaces
• Topology of Hitchin systems and Hodge theory of character varieties: the case A_1
• Introduction to Nonabelian Hodge Theory: flat connections, Higgs bundles and complex variations of Hodge structure
• Cohomology of large semiprojective hyperkaehler varieties
• Intersection cohomology of rank two character varieties of surface groups
• On the Kirwan map for moduli of Higgs bundles
• Endoscopic decompositions and the Hausel-Thaddeus conjecture
• Cohomology of the moduli of Higgs bundles via positive characteristic
• The nilpotent cone in the Mukai system for rank 2 and genus 2
• An Enumerative Approach to $P=W$
• Counterexamples to hyperkahler Kirwan surjectivity
• On the intersection cohomology of the moduli of ${\mathrm{SL}}_n$-Higgs bundles on a curve
• Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs