Prof. Dr. Mark Andrea De Cataldo
Mathematics
External Senior Fellow
Marie S. Curie FCFP Fellow
September; May - July 2018
CV
Mark Andrea got his Ph.D. in mathematics from the University of Notre Dame in 1995. He has been a postdoc at Washington University in St. Louis, Max Planck Institute for Mathematics in Bonn, Harvard University. He joined the faculty of Stony Brook University in 1998. His long-term visits include the Institute for Advanced Study (Princeton), the MPI (Bonn), the University of Michigan (Ann Arbor). He works in algebraic geometry, more precisely on the top.ology of algebraic varieties and maps.
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 Research 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.