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**Sylvain Edward Cappell** (born 1946), a Belgian American mathematician and former student of William Browder at Princeton University, is a topologist who has spent most of his career at the Courant Institute of Mathematical Sciences at NYU, where he is now the Silver Professor of Mathematics.

Sylvain Cappell | |
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Born | 1946 (age 77–78) Brussels, Belgium |

Nationality | Belgian, American |

Alma mater | Princeton University Columbia University |

Awards | AMS Distinguished Public Service Award (2018) Guggenheim Fellowship (1989–90) Sloan Fellowship (1971–72) |

Scientific career | |

Fields | Mathematics |

Institutions | New York University |

Doctoral advisor | William Browder |

Doctoral students | Shmuel Weinberger |

He was born in Brussels, Belgium and immigrated with his parents to New York City in 1950 and grew up largely in this city.^{[1]} In 1963, as a senior at the Bronx High School of Science, he won first place in the Westinghouse Science Talent Search for his work on "The Theory of Semi-cyclical Groups with Special Reference to Non-Aristotelian Logic." He then graduated from Columbia University in 1966, winning the Van Amringe Mathematical Prize.^{[2]} He is best known for his "codimension one splitting theorem",^{[3]} which is a standard tool in high-dimensional geometric topology, and a number of important results proven with his collaborator Julius Shaneson (now at the University of Pennsylvania). Their work includes many results in knot theory (and broad generalizations of that subject)^{[4]} and aspects of low-dimensional topology. They gave the first nontrivial examples of topological conjugacy of linear transformations,^{[5]} which led to a flowering of research on the topological study of spaces with singularities.^{[6]}

More recently, they combined their understanding of singularities, first to lattice point counting in polytopes, then to Euler-Maclaurin type summation formulae,^{[7]} and most recently to counting lattice points in the circle.^{[8]} This last problem is a classical one, initiated by Gauss, and the paper is still being vetted by experts.^{[citation needed]}

In 2012 he became a fellow of the American Mathematical Society.^{[9]} Cappell was elected and served as a vice president of the AMS for the term of February 2010 through January 2013.^{[10]}^{[11]}
In 2018 he was elected to be a member of the American Academy of Arts and Sciences.^{[12]}

**^**"Responses to NYC DOE questionnaire".*nychold.org*. Archived from the original on 2004-07-18.**^**"CCT Donors 2009–10 | Columbia College Today".*www.college.columbia.edu*. Retrieved 2022-06-04.**^**Cappell, Sylvain (1975), "A splitting theorem for manifolds",*Inventiones Mathematicae*,**33**(2): 69–170, Bibcode:1976InMat..33...69C, doi:10.1007/bf01402340, S2CID 121348951.**^**Cappell, Sylvain; Shaneson, Julius (1974), "The codimension two placement problem and homology equivalent manifolds",*Annals of Mathematics*,**99**(2): 277–348, doi:10.2307/1970901, JSTOR 1970901.**^**Cappell, Sylvain & Shaneson, Julius (1981), "Non-linear Similarity",*Annals of Mathematics*,**113**(2): 315–355, doi:10.2307/2006986, JSTOR 2006986.**^**Weinberger, Shmuel (1994),*The Topological Classification of Stratified Spaces*, Chicago: University of Chicago Press, ISBN 0-226-88566-6.**^**Shaneson, Julius (1995), "Characteristic classes, lattice points, and Euler-MacLaurin formulae",*Proc. International Congress of Mathematicians, vol 1 (Zurich 1994)*, Basel, Berlin: Birkhäuser, pp. 612–624.**^**Cappell, Sylvain & Shaneson, Julius (2007). "Some problems in number theory I: The Circle Problem". arXiv:math/0702613..**^**List of Fellows of the American Mathematical Society, retrieved 2012-11-10.**^**"2009 Election Results" (PDF). American Mathematical Society. Retrieved 2017-09-09.**^**"AMS Officers". American Mathematical Society. Archived from the original on 2013-01-25.**^**"Member Directory | American Academy of Arts and Sciences".

- "Official website at NYU".
- Sylvain Cappell at the Mathematics Genealogy Project