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Brief History
Academic: BSc (Hons in Computer Science), University of New South
Wales, 1983. MCom (Information Systems), University of New South Wales,
1990. Master of Science and Technology by coursework in Mathematics,
University of New South Wales, 2002.
Doctor of Philosophy in Applied Mathematics, University of New South Wales, 2007,
supervised by Professor
Ian Sloan and Associate
Professor Rob Womersley.
Working: Telecom Australia 1983-1986 - Computer Systems Officer.
Memorex-Telex 1986-1990 - Systems Engineer. Travel Industries Automated
Systems 1990-1995 - Systems Analyst. Accenture 1995-2001 - Consultant.
UNSW 2001-2002 - Research assistant programmer, Mathematics.
University of Sydney 2005-2006 - Scientific Computing Officer, Physics.
Research Interests
- Empirical testing of pseudo-random number generators
- Approximation on the sphere
- Object-oriented numerical analysis
- Applications of ScaLAPACK
- Clifford algebras
Teaching
PhD Thesis
Distributing points on the sphere: Partitions, separation, quadrature and energy
, UNSW, 2007.
Accompanying
Thesis/Dissertation Sheet.
Presentations
-
Practical computation with Clifford algebras, 2002.
-
A generic library of universal Clifford algebra templates, (poster) 2002.
-
Quick introduction to Clifford algebras, 2003.
-
A generalized FFT for Clifford algebras, 2003.
-
The Coulomb energy of spherical designs on S^2, 2003.
-
A partition of the unit sphere into regions of equal area and small diameter, 2004.
-
Partitions of the unit sphere into regions of equal area and small diameter, 2005.
- Movie of the partition EQ(3,99)
[MS MPEG4 V2 AVI file],
[MPEG4 file],
[MPEG4 Quicktime MOV file], 2006.
-
The Riesz energy of point sets on the unit sphere under weak-star convergence, 2005.
- Positive quadrature on the sphere and conjectures on monotonicities of Jacobi polynomials,
DWCAA06,
AustMS06, 2006.
- Spherical codes with good separation, discrepancy and energy,
HDA07,
ICIAM07,
AustMS07,
2007.
HDA07 talk handout, 2007.
-
Porting a sphere optimization program from LAPACK to ScaLAPACK,
CTAC08, 2008.
-
Testing the tests: using pseudorandom number generators to improve empirical tests,
MCQMC 2008.
-
Martin Albrecht,
Synergy Effects: a Sage introduction,
updated and edited by Paul Leopardi,
CLUG, 2008.
-
Approximating functions in Clifford algebras,
ANZMC 2008.
-
Accurate computation of the variance of the number of missing words in a random string,
4ICC 2008.
-
Quadrature using sparse grids on products of spheres,
HDA 2009.
-
Polynomial interpolation on the sphere, reproducing kernels and random matrices,
MASCOS Workshop on Stochastics and Special Functions 2009.
Publications and preprints
- Paul Leopardi,
"Conversion of a Sphere Optimization Program from LAPACK to ScaLAPACK",
(unpublished draft, 2002).
- Paul Leopardi,
"A generalized FFT for Clifford algebras",
Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 11, Number 5, 2005, pp. 663-688.
MR 2130632.
Preprint:
UNSW Applied Mathematics Report AMR04/17, March 2004.
- Kerstin Hesse, Paul Leopardi,
"The Coulomb energy of spherical designs on S^2",
Advances in Computational Mathematics,
Volume 28, Number 4 / May, 2008
, pp. 331-354.
DOI 10.1007/s10444-007-9026-7.
MR 2390282.
Preprint:
UNSW Applied Mathematics Report AMR04/34, December 2004, updated July 2005.
- Paul Leopardi,
"A partition of the unit sphere into regions of equal area and small diameter",
Electronic Transactions on Numerical Analysis, Volume 25, 2006,
pp. 309-327.
MR 2280380.
Preprint:
UNSW Applied Mathematics Report AMR05/18, May 2005, updated June 2006.
- Paul Leopardi,
"Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials",
DWCAA06 proceedings, Numerical Algorithms, Volume 45, Numbers 1-4 / August, 2007,
pp. 75-87.
DOI 10.1007/s11075-007-9073-7.
MR 2355973.
Preprint:
UNSW Applied Mathematics Report AMR06/41, December 2006.
- Walter Gautschi, Paul Leopardi,
"Conjectured inequalities for Jacobi polynomials and their largest zeros",
DWCAA06 proceedings, Numerical Algorithms, Volume 45, Numbers 1-4 / August, 2007,
pp. 217-230.
DOI 10.1007/s11075-007-9067-5.
MR 2355984.
Preprint:
UNSW Applied Mathematics Report AMR07/21, February 2007.
- Paul Leopardi,
"Diameter bounds for equal area partitions of the unit sphere",
Electronic Transactions on Numerical Analysis, Volume 35, 2009,
pp. 1-16.
Preprint:
December 2007 (revised January 2009).
- Paul Leopardi, Rob Womersley,
"Porting a sphere optimization program from LAPACK to ScaLAPACK",
ANZIAM Journal,
50 (CTAC2008),
November 2008, pp. C204-C219.
Preprint:
Revised, October 2008.
Figure 1:
TG,
TF.
Figure 2:
TI,
TT.
- Paul Leopardi,
"Testing the tests: using random number generators to improve empirical tests",
MCQMC 2008 proceedings (accepted).
Preprint:
May 2009.
Integer sequences
- A129337:
Maximal possible degree of a Chebyshev-type quadrature formula with n nodes, in the case of the constant weight function on [ -1,1], May 2007.
- A152139:
Correlation classes of pairs of different words, November 2008.
- A152959:
Number of correlation classes for pairs of different words in an alphabet of size 4, December 2008.
Conference organization
Software
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