Carlos Simpson

Carlos Tschudi Simpson (born 30 June 1962) is an American mathematician, specializing in algebraic geometry.

Simpson received his PhD in 1987 from Harvard University, where he was supervised by Wilfried Schmid; his thesis was entitled Systems of Hodge Bundles and Uniformization.^[1] He became a professor at the University of Toulouse III (Paul Sabatier University) and then at the University of Nice. He is research director of CNRS.

He works on module spaces of vector bundles, higher non-abelian de Rham cohomology (Hodge theory), the theory of higher categories and computer verification of mathematical proofs (e.g. verification of proofs within Zermelo–Fraenkel set theory using Coq). In his PhD dissertation, Simpson studied the notion of system of Hodge bundles, which can be seen as a special case of the higher dimensional generalization of Higgs bundles introduced earlier by Nigel Hitchin.^[2]

The Deligne-Simpson Problem, an algebraic problem associated with monodromy matrices, is named after Carlos Simpson and Pierre Deligne.^[3]

Simpson was an Invited Speaker with talk Nonabelian Hodge theory at the International Congress of Mathematicians in 1990 at Kyoto. In 2015 he received the Sophie Germain Prize.

Selected publications

• Constructing variations of Hodge Structure using Yang–Mills Theory and applications to Uniformization. J. AMS 1, 1988, 867–918.
• Transcendental Aspects of the Riemann–Hilbert Correspondence. Illinois J. Math., 34, 1990, 368–391.
• Harmonic bundles on noncompact curves. J. AMS 3, 1990, 713–770.
• Higgs bundles and local systems. Pub. Math. IHES 75, 1992, 5–95, numdam.
• Moduli of representations of the fundamental group of a smooth projective variety. 1,2, Pub. Math. IHES, vol. 79, 1994, 47–129, vol. 80, 1994, 5–79.
• Subspaces of moduli spaces of rank one local systems. Annales scientifiques de l'École Normale Supérieure, Sér. 4, vol. 26, 1993, 361–401.
• Asymptotic behavior of monodromy: singularly perturbed differential equations on a Riemann surface. Lecture Notes in Mathematics, Springer Verlag, 1991.
• Homotopy Theory of Higher Categories: From Segal Categories to N-Categories. Cambridge University Press, 2012.
• The Hodge Filtration on nonabelian cohomology. Algebraic geometry, Santa Cruz 1995, Proc. Sympos. Pure Math., 62, Part 2, A.M.S. (1997), 217–281.

References

1. Carlos Simpson at the Mathematics Genealogy Project
2. Steven Bradlow, Oscar García-Prada, Peter Gothen What is a Higgs bundle ?, Notices AMS, 54, 2007, 980, pdf
3. Vladimir Kostov The Deligne–Simpson Problem. A survey, 2002

External links

• Carlos Simpson's homepage at the University of Nice
• Carlos Simpson – An overview of the structure at infinitiy of representation spaces – YouTube, 2014