Toby Christopher O'Neil

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Current Position

Lecturer in Analysis at the Open University; joined October 1999.

Date of Birth

8 June 1970




1988 to 1991
University of Bristol
First Class BSc(Hons) in Mathematics
Received Hasse Prize (1991) for best final year mathematics undergraduate
1991 to 1994
University College London
Research leading to PhD in Mathematics
Thesis: A local version of the projection theorem and
other results in geometric measure theory
Supervisor: Professor D Preiss
Submitted October 1994, approved January 1995
Received Valerie Myerscough Travel Prize (1992)


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 R to 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 dimensionsUpdated 27/01/03, (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, to appear in Transactions of the AMS, ~30 published pages. [PDF] [PS] Updated 06/10/2006
  12. Universal singular sets in the calculus of variationsNew 08/09/2006, (with Marianna Csörnyei, Bernd Kirchheim, David Preiss and Steffen Winter), to appear in the Archive of Rational Mechanics, ~67 pages. [PDF] [PS]

Conference Reports

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

Other Publications

  1. An article about geometric measure theory which appeared in Supplement III of the Kluwer Encyclopedia of Mathematics, 2002. [PDF] [PS] Online version available at Springer Online Reference Works.
  2. How big is the Milky Way?, appeared in Plus Magazine, an online maths magazine for sixth formers, 2001.
  3. A review of Techniques in Fractal Geometry in Proceedings of the Edinburgh Mathematical Society, 1998.

Invited Lectures

Conference Talks

Other Talks


Teaching at the Open University

Organisational responsibilities

Contributions to teaching materials

Contributions to teaching methods and student support

Other Teaching Related Activity

Summer 2001 Lecturer at University of Cambridge Science Summer School.

April 2002 External PhD examiner, University of Jyväskylä, Finland.

May 2006 External MPhil examiner, The University of St Andrews.

Administration and Management at the Open University

June 2006 to present Elected member of University Senate.

May 2006 to present Member of faculty Course life review panel.

August 2005 to March 2006 User representative on new building project.

July 2005 to December 2005 Deputy head of department.

Spring 2005 to present Member of academic rewards advisory committee.

Autumn 2004 to present Member of OU TeX Group.

2003 Member of faculty web steering group.

Created:2 October 1996
Modified:24 May 2007

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