As you can see by looking at the list below, I'm a real analyst concentrating on problems in geometric measure theory, fractals and real analysis. If you are interested in any of these topics and want to learn more, then please send me an email - I'd be delighted to hear from you!

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Research Papers

1. A measure with a large set of tangent measures, Proc. Amer. Math. Soc.123 (1995) 2217-2220.
2. Vector-valued multifractal measures, (with K.J.Falconer), Proc. R. Soc. Lond. A, 452 (1996) 1433-1457. [PDF] [PS]
3. A local version of the projection theorem, Proc. Lond. Math. Soc., 73 (1996) 68-104. [PDF] [PS]
4. The multifractal spectrum of quasi self-similar measures, J. Math. Analysis and Appl., 211 (1997) 233-257.
5. Convolutions and the geometry of multifractal measures, (with K.J.Falconer), Mathematische Nachrichten, 204 (1999) 61-82.
6. The multifractal spectrum of projected measures in Euclidean spaces, Chaos, Solitons and Fractals, 11 (2000) 901-921.
7. $$N$$-fold sums of Cantor Sets, (with K E Hare), Mathematika, 47 (2000) 243-250. [PDF] [PS]
8. Graphs of continuous functions from $$\mathbb{R}$$ to $$\mathbb{R}$$ are not purely unrectifiable, Real Analysis Exchange, 26 (2001) 445-447. [PDF] [PS]
9. The composition of two derivatives has a fixed point, (with M Csörnyei and D Preiss), Real Analysis Exchange, 26 (2001) 749-760. [PDF] [PS]
10. Visible parts and dimensions, (with Esa Järvenpää, Maarit Järvenpää and Paul MacManus), Nonlinearity,16 (2003) 803-818. [PDF] [PS]
11. The Hausdorff dimension of visible sets of planar continua, Transactions of the AMS 359 Number 11 (2007), 5141-5170. [journal electronic version] [PDF] [PS]
12. Universal singular sets in the calculus of variations, (with Marianna Csörnyei, Bernd Kirchheim, David Preiss and Steffen Winter), Archive of Rational Mechanics 190 Number 3 (2008), 371-424. [PDF] [PS]
13. Points of middle density in the real line, (with M Csörnyei and J Grahl), Real Analysis Exchange 37(2) (2012) 243-248. [PDF] [PS]

Conference Reports

1. The dimension of visible sets, Real Analysis Exchange 28th Summer Symposium Conference Reports, June 2004. 4 pages. [PDF] [PS]
2. Singular sets in the calculus of variations, Real Analysis Exchange 30th Summer Symposium Conference Reports, June 2006. 4 pages. [PDF] [PS]

Other Publications

1. How big is the Milky Way?, appeared in Plus Magazine, an online maths magazine for sixth formers. June 2001.
2. An article about geometric measure theory that appeared in Supplement III of the Kluwer Encyclopedia of Mathematics, 2002. [PDF] [PS]. An online version is available.
3. A review of Techniques of Fractal Geometry which appeared in the Proceedings of the Edinburgh Mathematical Society. [PDF] [PS]

Created:13 August 1996
Modified:9 November 2012

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