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Paul Leopardi Graduate student School of Mathematics and Statistics University of New South Wales

Brief History Research interests PhD Thesis Presentations Preprints Conferences Software

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. Currently a part-time PhD student in Applied Mathematics supervised by Professor Ian Sloan and Associate Professor Rob Womersley, and working full-time at the School of Physics at the University of Sydney.

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. USyd 2005-2006 - Scientific Computing Officer.

• Empirical testing of pseudo-random number generators
• Approximation on the sphere
• Object-oriented numerical analysis
• Applications of ScaLAPACK
  
• Clifford algebras

• 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, 2007. (Talk handout, 2007).

• Paul Leopardi, "A generalized FFT for Clifford algebras", Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 11, Number 5, 2005, pp. 663-688.
  Preprint: Applied Maths Report AMR04/17, March 2004.
• Kerstin Hesse, Paul Leopardi, "The Coulomb energy of spherical designs on S^2", Advances in Computational Mathematics, DOI 10.1007/s10444-007-9026-7, 2007.
  Preprint: Applied Maths 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.
  Preprint: Applied Maths Report AMR05/18, May 2005, updated June 2006.
• Paul Leopardi, "Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials", Numerical Algorithms, DOI 10.1007/s11075-007-9073-7, 2007.
  To appear in DWCAA06 proceedings in Numerical Algorithms.
  Preprint: Applied Maths Report AMR06/41, December 2006.
• Walter Gautschi, Paul Leopardi, "Conjectured inequalities for Jacobi polynomials and their largest zeros", Numerical Algorithms, DOI 10.1007/s11075-007-9067-5, 2007.
  To appear in DWCAA06 proceedings in Numerical Algorithms.
  (Preprint)

• Clifford minisymposia at ICIAM 2003

• GluCat: Generic library of universal Clifford algebra templates
• EQSP: Recursive Zonal Equal Area Sphere Partitioning Toolbox

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