Sylvain E. Cappell

New York University
Mathematical and Physical Sciences
Mathematics, Applied Mathematics, and Statistics


Professor Sylvain E. Cappell is the Silver Professor of Mathematics at New York University. Cappell's codimension 1 splitting theory for manifolds of dimension at least 5 yielded the first proofs of the Novikov conjecture for a wide class of groups and were critical to Farrell-Hsiang's proof of Borel's conjecture. Cappell-Shaneson's homology surgery theory completely changed knot theory and had many other applications. Cappell-Shaneson gave the first examples of topologically conjugate but linearly distinct orthogonal matrices. Cappell-Weinberger's classification of supernormal'' singular spaces paralleled high dimensional manifold theory. Cappell-Shaneson's characteristic class formula, when applied to toric varieties, gave lattice point counting formulae, deeply generalizing Pick's theorem, finally explaining'' the critical role of Bernoulli numbers in topology. He received the 2018 AMS Award for Distinguished Public Service for his remarkable mentoring of talented young mathematicians, his dedication to protecting human rights, and his extraordinary involvement in outreach. 

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