Selected Publications
- A support theorem for the Hitchin fibration: the case of SL_n, to appear in Compositio math.
- Topology of Hitchin systems and Hodge theory of character varieties: the case A1 (with T. Hausel and L. Migliorini), Annals of Mathematics 175 (2012), 1329-1407.
- The perverse filtration and the Lefschetz Hyperplane Theorem (with L. Migliorini), Annals of Mathematics, Vol. 171, No. 3, 2010, 2089-2113.
- The Hodge theory of algebraic maps (with L. Migliorini), Ann. Scient. Ec. Norm. Sup., 4e serie, t.38, 2005, p. 693-750.
FRIAS Project
Support and symmetries for Hitchin fibrations.
The Hitchin fibration is of fundamental importance in algebraic geometry, number theory and representation theory. I propose to determine the supports of Hitchin fibrations and to establish and explain certain remarkable hidden symmetries, P=W and TMS, on the cohomology of the moduli spaces of Higgs bundles.