Toby Christopher O'Neil
CV
Current Position
Lecturer in Analysis at the Open University; joined October 1999.
Date of Birth
8 June 1970
Nationality
British
Education
 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
Research Papers
 A measure with a large set of tangent measures, Proc. Amer. Math. Soc.123 (1995) 22172220.
 Vectorvalued multifractal measures, (with K.J.Falconer), Proc. R. Soc. Lond. A, 452 (1996) 14331457. [PDF] [PS]
 A local version of the projection theorem, Proc. Lond. Math. Soc., 73 (1996) 68104. [PDF] [PS]
 The multifractal spectrum of quasi selfsimilar measures, J. Math. Analysis and Appl., 211 (1997) 233257.
 Convolutions and the geometry of multifractal measures, (with K.J.Falconer), Mathematische Nachrichten, 204 (1999) 6182.
 The multifractal spectrum of projected measures in Euclidean spaces, Chaos, Solitons and Fractals, 11 (2000) 901921.
 Nfold sums of Cantor Sets, (with K E Hare), Mathematika, 47 (2000) 243250. [PDF] [PS]
 Graphs of continuous functions from R to R are not purely unrectifiable, Real Analysis Exchange, 26 (2001) 445447. [PDF] [PS]
 The composition of two derivatives has a fixed point, (with M Csörnyei and D Preiss), Real Analysis Exchange, 26 (2001) 749760. [PDF] [PS]
 Visible parts and dimensions^{Updated 27/01/03}, (with Esa Järvenpää, Maarit Järvenpää and Paul MacManus), Nonlinearity,16 (2003) 803818. [PDF] [PS]
 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
}
 Universal singular sets in the
calculus of variations^{New
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
 The dimension of visible sets,
Real Analysis Exchange 28th Summer Symposium
Conference Reports, June 2004.
[PDF]
[PS]
 Singular sets in the calculus of variations,
Real Analysis Exchange 30th Summer Symposium Conference Reports, to appear. [PDF] [PS]
Other Publications
 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.
 How big is
the Milky Way?, appeared in
Plus
Magazine, an online maths magazine for sixth formers, 2001.
 A review of Techniques in Fractal Geometry in
Proceedings of the Edinburgh Mathematical Society, 1998.
Invited Lectures
 May 1995, University of Edinburgh, A local version of the BesicovitchFederer projection theorem.
 April 1996, University of North Texas, Quasi selfsimilar multifractal measures.
 August 1997, University of Jyvaskyla, Projections of multifractal measures.
 February 1998, University of Edinburgh, Geometric measure theory, singular integrals and removable sets.
 November 1998, University of Maynooth, Projections of sets and measures in Euclidean spaces.
 April 1999, Rice University, A local version of the BesicovitchFederer Projection Theorem.
 May 2000, University of Jyvaskyla, Some results in geometric measure theory.
 June 2000, Imperial College, London, Recent Problems and Results in Geometric Measure Theory.
 January 2001, University of Manchester, The dimension of the visible part of a set and other results.
 April 2002, University of Jyväskylä,
The dimension of the visible parts of a set.
 October 2003, University of Oxford,
Dimension of visible sets in the plane.
 November 2003, University of Bath,
The dimension of the visible parts of a set.
 October 2004, University of Edinburgh,
How much of a set can you see?
 October 2004, University of Oxford,
Universal singular sets.
 March 2006, University of Birmingham, Universal singular sets in the Calculus of Variations.
 May 2006, University of Glasgow, Singular sets in the Caculus of Variations.
Conference Talks
 September 1992, 5th Conference in Real Analysis and Measure Theory, Italy, A measure with a large set of tangent measures
 June 1994, Fractal Geometry and Stochastics, Germany, A local version of the BesicovitchFederer projection theorem
 May 1995, Ergofract 95, Spain, Vectorvalued multifractal measures
 October 1995, Weekend Analysis Seminar in Weinberg, Austria, A local version of the BesicovitchFederer projection theorem
 January 1997, 25th Winter School in Abstract Analysis, Czech Republic, The multifractal spectrum of projected measures
 August 1997, Conference in Number Theory and Dynamical Systems, University of York, Projections of multifractral measures
 August 1998, Fractal Geometry and Stochastics II, Germany, The multifractal spectra of projected measures
 August 2000, Summer school on Geometric and Dynamical Aspects of Measure Theory, Hungary, The dimension of visible sets
 February 2001, 29th Winter school in Abstract Analysis, Czech Republic, The composition of two derivatives has a fixed point
 March 2003, Fractal Geometry and Stochastics III, Germany, The Hausdorff dimension of the visible sets of connected compact sets
 April 2003, 55th British Mathematical Colloquium, Birmingham, The dimension of the visible sets of compact connected sets in the plane
 July 2003, Analysis and Geometric Measure Theory, Banff, Canada, The dimension of visible sets
 January 2004, 32nd Winter School in Abstract Analysis,
The dimension of the visible parts of a set, Czech Republic.
 June 2004, 28th Summer Symposium in Real Analysis,
The dimension of visible sets, Slippery Rock University, USA.
 January 2005, 33rd Winter School in Abstract Analysis,
Universal sets in the calculus of variations, Czech Republic.
 June 2006, 30th Summer Symposium in Real Analysis,
Singular sets in the calculus of variations, University of
North Carolina at Asheville, USA.
 August 2007 (forthcoming),
Real Analysis, Geometric Measure Theory, PDE and Banach Spaces Conference, Warwick, UK.
Other Talks
 October 2005, Talk to Cambridge Undergraduate Mathematics Society, The Archimedeans,
How
big is the Milky Way?, Cambridge, UK.
Other
Organisational responsibilities

M338 Topology (30 points)
2007 
Coordinator of Diagnostic Quiz 

2005  present 
Course Team Chair (Presentation) and E & A Board Chair.
Responsible for coordinating assessment for first and subsequent presentations. 

2005  2006 
Deputy Course Team Chair (Production).
Responsible for overseeing final steps of production, ensuring quality and timeliness of material handovers. 

2004  2006 
Blockcoordinator.
Responsible for overseeing teaching strategy and coordinating storyline of course materials. 

2003  2005 
Academic Coordinator for software. 

Responsible for defining content and structure of twothirds of software.
(23 hours study time) 

M337 Complex Analysis (30 points)
2004 
Course Team Chair (Presentation), E & A Board Chair. 

Responsible for overseeing production of assessment material,
and for producing Course Life Review Report
(resulting in life of course being extended to 2009).

M203 Introduction to Pure Mathematics (60 points)
2001 & 2005 
Course Director of summer school. (Two weeks total.) 
Contributions to teaching materials

M338 Topology (30 points)
2005  present 
Author of 2 TMAs (half of continuous assessment)
per year, and main author of exam papers (twothirds of content). 
2000  2006 
Primary author of 7 units (~ 350 pages, ~ 120 study hours). 
2000  2006 
Critical reader of all units and text (13 units, ~ 650 pages). 
2002  2006 
Author of half of the Exercise Book for whole course (35 pages). 
2005 
Author of half of Computing Guide (15 pages, 2 study hours). 
2005 
Author and Presenter of audio
component for onethird of computer software (40 minutes). 
2004 
Academic Editor of one unit. Responsible for
checking correctness and consistency of mathematical content. 

M208 Pure Mathematics (60 points)
2003  2005 
Critical Reader for Analysis blocks. (8 units, ~120 study hours) 

Responsible for advising on teaching of epsilondelta definition
of continuity to ensure consistency with the approach of M338. 

M435 Metric and Topological Spaces and
Geometric Topology (30 points)
2001  2004 
Member of E & A Board. 

Responsible for checking of TMA and examination questions for correctness. 

M835 Fractal Geometry (30 points)
2000 
Critical Reader of all course materials. 

Responsible for advising and checking
correctness of all course notes and exercises. 

M337 Complex Analysis(30 points)
1999  present 
Member of E & A Board, responsible for authoring at least one TMA per year. 
2000 
Author of Diagnostic Quiz (half a unit) to
help potential students determine whether they are
ready for the course. Still in use today. 

MST121/MS221 Using Mathematics/Exploring Mathematics rewrite
(60 points)
1999  2001 
Critical Reader of all course texts (~30 units). 
2000 
Presenter of audio commentary (30 minutes) on calculus for MST121. 
Contributions to teaching methods and student support

M338 Topology (30 points)
2006 
Regular participant in student FirstClass course conference. 

Organiser of FirstClass tutor conference. 

Organiser and main speaker at tutor briefing on launch of M338. 
2005 
Responsible for TMA assessment strategy:
one short TMA early on in the course designed to
allow fast (formative) feedback. 
2004 
Devisor of computerbased software for
teaching of epsilondelta definition of continuity. 

M337 Complex Analysis
(30 points)
2007 
Moderator of student FirstClass conference. 

M203 Introduction to Pure Mathematics
(60 points)
1999  2005 
Tutor at summer school. (Two weeks each year.) 

M431 The Lebesgue Integral
(30 points)
2000 
Associate Lecturer for final course presentation. 

Other
2002 
Internal examiner, PhD Thesis (John Wordsworth). 
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
Back up to the introduction.