Recent E-prints:

• (with T. R. Riley) Some duality conjectures for finite graphs and their group theoretic consequences [1 March 2003; revised 11 August 2004, to appear in Proc. Edin. Math. Soc.]: .pdf.
  This is the second of 3 projected papers on filling length. It concerns statements of the graph theoretic Conjecture H and its group theoretic consequences. The ``electrostatic model" for central extensions is introduced and it is shown how it enables one to estimate filling functions with the aid of Conjecture H. Various other filling functions are introduced and are shown to agree with filling length up to equivalence, under the assumption of Conjecture H. Finally we examine consequences of uniformly bounded vertex valences in van Kampen diagrams on filling functions, which is the analog in geometry of curvature bounded away from negative infinity.
  The third paper in the series will be devoted to the proof of Conjecture H.
• (with T. R. Riley) The gallery length filling function and a geometric inequality for filling length [25 January 2003, revised 27 May 2005], accepted for publication in Proc. London. Math. Soc.: .pdf
  This is the first of 3 projected papers on filling length in group theory, as the analogue of "space" in computer science, its calculation using duality of planar graphs, and its relation with isoperimetric inequalities for central extensions. The first paper contains a new proof of the double exponential theorem based on duality, using estimates of the new filling function, gallery length, introduced here.
• (with D. F. Holt and T. R. Riley) Isoperimetric inequalities for nilpotent groups .pdf (appeared in GAFA, Geom. Funct. Anal. 13 (2003), no. 4, 795--814).
  This paper contains the first complete proof of the "c+1" theorem, that states that every finitely generated nilpotent group of nilpotence class c has an isoperimetric polynomial of degree c+1.
• (with T. R. Riley) Filling radii of finitely presented groups .pdf (appeared in Quart. J. Math., Oxford, 53 No. 1 (2002) 31-45).
• (with T. R. Riley) Filling length in finitely presentable groups .pdf (appeared in Geom. Ded. 92 No. 1 (2002) 41-58). This paper contains fundamental results about the filling length, which plays the same role to "space" in computer science that area plays to "time". It is shown that the filling length is bounded by the product of the filling diameter and the logarithm of the filling area, where both are calaculated on the same van Kampen fillings.
• (with H. B. Short) Some isoperimetric inequalities for kernels of free extensions .pdf (appeared in Geom. Ded. 92 No. 1(2002) 63-72). A finitely presented group which occurs as the kernel of a homomorphism of a hyperbolic group to a free group satisfies a polynomial isoperimetric inequality.