Sylvain Cappell

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Sylvain Cappell
Born 1947
Belgium
Education Princeton University
Occupation mathematician
Website
http://www.math.nyu.edu/faculty/cappell/

Sylvain Cappell, Belgian-born American mathematician (born 1947), a former student of William Browder at Princeton, is a topologist who has spent most of his career at the [[Courant Institute of the Mathematical Sciences]] at NYU.

He is best known for his "codimension one splitting theorem" [1], 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) [2] and aspects of low-dimensional topology. They gave the first nontrivial examples of topological conjugacy of linear transformations [3], which led to a flowering of research on the topological study of spaces with singularities [4].

More recently, they combined their understanding of singularities, first to lattice point counting in polytopes, then to Euler-Maclaurin type summation formulae [5], and most recently to counting lattice points in the circle [6]. This last problem is a classical one, initiated by Gauss and the paper is still being vetted by experts.

[edit] Awards

[edit] References

  1. ^ Sylvain Cappell, A splitting theorem for manifolds, Inventiones Mathematicae, 33 (1975) pp 69-170
  2. ^ Sylvain Cappell and Julius Shaneson, The codimension two placement problem and homology equivalent manifolds, Annals of Math. 99 (1974) 277-348.
  3. ^ Sylvain Cappell and Julius Shaneson, Nonlinear Similarity, Annals of Math. 113 (1981) 315-355
  4. ^ Shmuel Weinberger, The Topological Classification of Stratified Spaces, University of Chicago Press, Chicago, 1994
  5. ^ Julius Shaneson, Characteristic classes, lattice points, and Euler-MacLaurin formulae, Proc. International Congress of Mathematicians, vol 1 (Zurich 1994) 1995 Birkhauser, Basel, Berlin, 612-624
  6. ^ Sylvain Cappell and Julius Shaneson, Some problems in number theory I: The Circle Problem, http://front.math.ucdavis.edu/0702.5613
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