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

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1987 from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where he was supervised by

Wilfried Schmid Wilfried Schmid (born May 28, 1943) is a German-American mathematician who works in Hodge theory, representation theory, and automorphic forms. After graduating as valedictorian of Princeton University's class of 1964, Schmid earned his Ph.D. at ...

; his thesis was titled ''Systems of Hodge Bundles and Uniformization''. He became a professor at the University of Toulouse III (

Paul Sabatier University Paul Sabatier University (''Université Paul Sabatier'', UPS, also known as Toulouse III) is a French public university, in the Academy of Toulouse. It is one of the several successor universities of the University of Toulouse. Toulouse III was ...

) and then at the

University of Nice A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the ...

. He is research director of the

Centre national de la recherche scientifique The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science Basic research, also called pure research o ...

. He works on moduli spaces of

vector bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every po ...

s, higher non-abelian de Rham cohomology (

Hodge theory In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohom ...

), the theory of higher categories and computer verification of mathematical proofs (''e.g.'' verification of proofs within

Zermelo–Fraenkel set theory In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as ...

using

Coq Coq is an interactive theorem prover first released in 1989. It allows for expressing mathematical assertions, mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof ...

). In his Ph.D. dissertation, Simpson studied the notion of system of

Hodge bundle In mathematics, the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves. Furthermore, it has applications to the theory of modular forms on r ...

s, which can be seen as a special case of the higher dimensional generalization of

Higgs bundle In mathematics, a Higgs bundle is a pair (E,\varphi) consisting of a holomorphic vector bundle ''E'' and a Higgs field \varphi, a holomorphic 1-form taking values in the bundle of endomorphisms of ''E'' such that \varphi \wedge \varphi=0. Such pai ...

s introduced earlier by

Nigel Hitchin Nigel James Hitchin FRS (born 2 August 1946) is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University o ...

. The Simpson correspondence (or the Corlette-Simpson correspondence, named after Kevin Corlette and Simpson) is a correspondence between Higgs bundles and representations of the

fundamental group In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of ...

of a smooth, complex

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane c ...

. The Deligne–Simpson Problem, an algebraic problem associated with monodromy matrices, is named after Carlos Simpson and

Pierre Deligne Pierre René, Viscount Deligne (; born 3 October 1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Pr ...

. Simpson was an Invited Speaker with talk ''Nonabelian Hodge theory'' at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1990 at

Kyoto Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...

. In 2015 he received the

Sophie Germain Prize The Sophie Germain Prize (in French: ''Prix Sophie Germain'') is an annual mathematics prize from the French Academy of Sciences conferred since the year 2003. It is named after the French mathematician Sophie Germain, and comes with a prize of � ...

Selected publications

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References

External links

* * * {{DEFAULTSORT:Simpson, Carlos 1962 births Living people 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni Academic staff of the University of Toulouse Academic staff of Côte d'Azur University Algebraic geometers Topologists