Stephen J. Bigelow

from Wikipedia, the free encyclopedia
Stephen Bigelow.jpg

Stephen John Bigelow (born September 1971 in Cambridge ) is a British mathematician . He is a professor at the University of California, Santa Barbara .

Life

Bigelow graduated from the University of Melbourne with a bachelor's degree in 1992 and a master's degree in 1994 and received his PhD from the University of California, Berkeley with Robion Kirby in 2000 . In 2002 he became an Assistant Professor and in 2007 an Associate Professor at the University of California, Santa Barbara.

He deals with knot theory , braid groups and their representation theory and low-dimensional topology. He proved in 2001 (and independently proved this to Daan Krammer ) that the braid groups are linear. In doing so, they used the Lawrence-Krammer representation of braid groups and proved that the braid groups can be represented as subgroups of the general linear group over the complex numbers by suitable choice of the parameters in this representation . Bigelow thus solved a long open problem. Faithful, linear, finite-dimensional representations of groups of braids were known only in a few cases; Bigelow proved their existence.

In 2000 he received the Blumenthal Award from the American Mathematical Society (AMS). From 2002 to 2006 he was a Sloan Research Fellow . In 2013 he became a Fellow of the American Mathematical Society. In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (Representation theory of braid groups).

Fonts

  • The Burau representation is not faithful for n = 5. Geom. Topol. 3: 397-404 (1999).
  • Braid groups are linear. J. Amer. Math. Soc. 14 (2001), no. 2, 471-486
  • with Budney: The mapping class group of a genus two surface is linear. Algebr. Geom. Topol. 1 (2001), 699-708
  • Representations of braid groups. Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 37-45, Higher Ed. Press, Beijing, 2002.
  • A homological definition of the Jones polynomial, Geometry and Topology Monographs, Volume 4, Invariants of Knots and 3-Manfiolds (Kyoto 2001), 2002, pp. 29-41
  • Braid groups and Iwahori-Hecke algebras, Proceedings of Symposia in Pure Mathematics, 2006.
  • with Peters, Morrison, Snyder: Constructing the extended Haagerup planar algebra. Acta Math. 209 (2012), no. 1, 29-82.

Web links

Individual evidence

  1. ↑ Stephen J. Bigelow in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Bigelow, Braid groups are linear, Journal of the American Mathematical Society, 2000, Arxiv
  3. ↑ Arxiv
personal data
SURNAME Bigelow, Stephen J.
ALTERNATIVE NAMES Bigelow, Stephen John
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH September 1971
PLACE OF BIRTH Cambridge