Brian Bowditch

Brian Hayward Bowditch (* 1961 in Neath (Wales) ) is a British mathematician who studies differential geometry (Riemannian geometry, metric geometry), hyperbolic geometry and geometric group theory. He is a professor at the University of Warwick .

Life

Bowditch grew up in Port Talbot and studied mathematics at Cambridge University from 1979 to 1983 . He received his PhD in 1988 under David Epstein at the University of Warwick (Geometrical Finiteness for Hyperbolic Groups). As a post-doctoral student , he has been to the Institute for Advanced Studies , IHES , the University of Melbourne and the University of Aberdeen. From 1992 to 2007 he was at the University of Southampton , where he became a professor, and then at the University of Warwick.

He was a visiting scientist in Zurich, Auckland, Melbourne, Lille, Toulouse, Strasbourg, Bonn (Max Planck Institute for Mathematics), Dijon, at the Tokyo Institute of Technology, at the CRM in Barcelona, at the Isaac Newton Institute and the Bernoulli Center in Lausanne.

He transferred geometric finiteness theorems for Klein's groups of isometric groups of hyperbolic spaces in two and three dimensions to higher dimensions. In the 1990s he investigated the boundaries at infinity of hyperbolic groups (according to Mikhail Gromov ) and proved the Cut Point Conjecture that hyperbolic groups with one end have no globally separating points ("global cut points"). In 1998 he gave a topological characterization of hyperbolic groups via their group action on the edge ( convergence property ). It was already known before that the effect of the group on triples of different points of the edge is discontinuous and co-compact , Bowditch proved that conversely from this behavior it also follows that the group is a hyperbolic group, which Gromov had suspected. Bowditch also gave a new theory of JSJ decomposition that goes beyond the original one from Zlil Sela . In a paper published in 2012 but already written in the 1990s, he laid the foundations for the theory of relatively hyperbolic groups .

In 2006 he gave a new proof of the hyperbolicity of the complex of curves , first proven by Howard Masur , Yair Minsky in 1999. The complex of curves was introduced in 1978 by William James Harvey and plays a significant role in the study of mapping class groups and the geometry of the pond miller space .

In 2007, he solved the problem by Angel John Horton Conway from the combinatorial game theory . In the angel and devil game an angel of might k can take a maximum of k steps in the manner of a chess king on an infinite chessboard in each of the two directions per move, starting at the origin. In each turn, the devil removes a stone that the angel can jump over, but which he can no longer land on, and wins if the angel can no longer move. Berlekamp proved that the devil has a winning strategy for k = 1. Bowditch proved that a Powerful Angel has a winning strategy. Soon after, Andras Mathé and O. Kloster independently proved that a winning strategy for the angel also exists for k = 2.

In 1997 he received the Whitehead Prize . In 2004 he was invited speaker at the European Congress of Mathematicians in Stockholm (Hyperbolic 3-manifolds and the geometry of the curve complex).

Fonts

Geometrical finiteness for hyperbolic groups. J. Funct. Anal. 113: 245-317 (1993)
Geometrical finiteness with variable negative curvature. Duke Math. J., 77: 229-274 (1995).
Group actions on trees and dendrons. Topology, 37: 1275-1298 (1998)
Boundaries of strongly accessible hyperbolic groups. in: The Epstein birthday script, Geometry & Topology Monographs, vol. 1, Geom. Topol. Publ., Coventry, 1998, pp. 51-97
A topological characterization of hyperbolic groups. J. Amer. Math. Soc. 11: 643-667 (1998)
Cut points and canonical splittings of hyperbolic groups. Acta Math. 180: 145-186 (1998)
Intersection numbers and the hyperbolicity of the curve complex. J. pure angew. Math. 598 (2006), 105-129.
Tight geodesics in the curve complex. Invent. Math. 171 (2008), 281-300
Relatively hyperbolic groups. Boarding school J. Algebra Comput. 22 (2012), no. 3., 1250016, 66p.

Web links

Homepage

Individual evidence

^ Brian Bowditch in the Mathematics Genealogy Project (English)
↑ More precisely, he proved the conjecture for large classes of groups (published in 1998), the full proof followed shortly afterwards in 1996 by GA Swarup
^ Bowditch, The angel game in the plane, Combinatorics, Probability and Computing, Volume 16, 2007, 345-362. The problem was posed in Berlekamp, Conway, Guy Winning ways 1982 and more precisely by John Conway, The angel problem, in: Richard Nowakowski (ed.) Games of No Chance, MSRI Publications 29, 1996, pp. 3-12, pdf .

personal data
SURNAME	Bowditch, Brian
ALTERNATIVE NAMES	Bowditch, Brian Hayward (full name)
BRIEF DESCRIPTION	British mathematician
DATE OF BIRTH	1961
PLACE OF BIRTH	Neath (Wales)

[1] Brian Bowditch in the Mathematics Genealogy Project (English)

[2] More precisely, he proved the conjecture for large classes of groups (published in 1998), the full proof followed shortly afterwards in 1996 by GA Swarup

[3] Bowditch, The angel game in the plane, Combinatorics, Probability and Computing, Volume 16, 2007, 345-362. The problem was posed in Berlekamp, Conway, Guy Winning ways 1982 and more precisely by John Conway, The angel problem, in: Richard Nowakowski (ed.) Games of No Chance, MSRI Publications 29, 1996, pp. 3-12, pdf .