Jonathan M. Borwein

What Jon has to say about himself
Status: Director, Shrum Professor
Affiliation: Department of Mathematics and Statistics, SFU
Phone: (604) 291-3070/5617
Office: TLX10526


Research Interest

I am interested in various brands of analysis - Computational Analysis, Functional Analysis, Classical Analysis - in Number theory and in Optimization. I have three main research projects.

At CECM we are interested in developing methods for exploiting mathematical computation as a tool in the development of mathematical intuition, in hypotheses building, in the generation of symbolically assisted proofs, and in the construction of a flexible computer environment in which researchers and research students can undertake such research. That is in doing ``Experimental Mathematics''.
Convex and Nondifferentiable Analysis
Over the last twenty years great progress has been made in the provision of non-convex, non-differentiable analogues of traditional differentiable calculus - both in Euclidean spaces and in infinite dimensional spaces. This work provides powerful tools for the study of nonlinear phenomena in optimization, control, dynamical systems and elsewhere. The field also provides many fascinating theoretical and technical challenges.
Entropy Optimization Methods
Convex optimization methods and iterative algorithms involving projecions play a central role in the mathematization and practical solution of many important "inverse problems" such as arise in tomography, signal estimation, signal reconstruction and elsewhere. Analysis of these problems requires a blend of techniques from Convex Analysis, Approximation Theory, Functional Analysis and Measure Theory.


Selected Works

Experimental Mathematics:
Jonathan M. Borwein and Robert Corless, ``Emerging tools for experimental mathematics,'' MAA Monthly, 106 (1999), 889-909. [CECM Research Report 98:110].

Functional Analysis:
J.M. Borwein and W.B. Moors, ``Essentially smooth Lipschitz functions,'' Journal of Functional Analysis, 49 (1997), 305-351. [CECM Research Report 95:029]

Number Theory:
J.M. Borwein and D.M. Bradley, ``Empirically determined Apéry-like formulae for zeta(4n+3),'' Experimental Mathematics, 6 (1997), 181-194. [CECM Research Report 96:069]

Classical Analysis:
J. M. Borwein, D. M. Bradley, D. J. Broadhurst and P. Lisonek, ``Combinatorial aspects of multiple zeta values,'' Electronic Journal of Combinatorics, 5 (1998), R38, 12 pages.

H.H. Bauschke and J.M. Borwein, ``On projection algorithms for solving convex feasibility problems,'' SIAM Review, 38 (1996), 367-426.

M.N. Limber, A. Celler, J.S. Barney, M.A. Limber, J.M. Borwein, ``Direct Reconstruction of Functional Parameters for Dynamic SPECT,''IEEE Transactions on Nuclear Science, 42(1995), 1249-.

J.M. Borwein and A.S. Lewis, ``Partially-finite convex programming in tex2html_wrap_inline41 : entropy maximization,'' SIAM J. Optimization, 3 (1993), 248-267.

J.M. Borwein, P.B. Borwein, and D.A. Bailey, ``Ramanujan, modular equation s and pi or how to compute a billion digits of pi,'' MAA Monthly, 96 (1989), 201-219. (Awarded Chauvenet and Hasse prizes.)

Welcome to CECM
CECM Site Search

Advanced Search
Your name:

Your email address:

Your comments:
Permanent Members  |  Associate Members  |  Technical Associates  |  Visitors / Students  |  Past Members