Timothy Riley

Assistant Professor of Mathematics

Web Site www.math.cornell.edu/~riley/ Contact Information Office:  401 Malott Hall Phone:  (607) 255-4089 Fax:  (607) 255-7149 Email:  Courses & Office Hours

Education

Ph.D. (2002) Oxford University

Research Area: Geometric group theory

I work in geometric group theory. I study infinite discrete groups via associated metric spaces, Riemannian manifolds, graphs and cell complexes, and I focus on geometric features such as curvature, the shapes of balls, and characteristics of discs spanning loops (which can be called soap-film geometry). The setting for much of my research to date has been the geometry of the word problem for groups — a meeting-point of algebra, algorithmic complexity, geometry, topology and formal languages. My work has also touched on graph theory and cryptography.

Selected Publications

Higher connectedness of asymptotic cones, Topology 42 (2003), 1289–1352.

Isoperimetric inequalities for nilpotent groups (with Steve Gersten and Derek Holt), Geometric and Functional Analysis 13 (2003), 795–814.

The absence of efficient dual pairs of spanning trees in planar graphs (with Bill Thurston), Electronic J. Comb. 13, N13 (2006).

Diameters of Cayley graphs of Chevalley groups (with Martin Kassabov), Eur. J. Comb 28 no. 3 (2007), 791–800.

Filling functions; part II of Geometry of the Word Problem for Finitely Generated Groups, Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser-Verlag, 2007.

Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams (with Martin Bridson), Journal of Differential Geometry 82 no. 1 (2009), 115–154.

Last modified: July 15, 2009