Frontiers Lectures

October 13-17, 2003

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Michel Delfour, FRSC

Centre de recherches mathématiques
and

Département de Mathématiques et de Statistique
Université de Montréal, Montréal, Canada

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Lecture 1

From river blindness to interventional cardiology

Lecture 2

Shapes and geometries as design, optimization, or control variables

Lecture 3

Oriented distance function, geometry, and applications


1. Career sketch

Michel Delfour graduated in 1966 from McGill University where he received the Ernest Brown Gold Medal of the Faculty of Engineering for highest ability throughout the undergraduate course. Thanks to a Case Fellowship in 1968 he completed his Master Degree in Control Theory at the Systems Research Center of the Case Institute of Technology and published his first paper on the control of perturbed systems in the SIAM Journal of Control. Convinced of the central role of Mathematics in Engineering, he enrolled in the new program in Mathematical Systems Theory and completed his Ph.D. in Mathematics in 1970. His last year was spent at the Electronic Systems Laboratory of the Massachusetts Institute of Technology. In 1970 he joined the new Centre de Recherches Mathématiques of the Université de Montréal founded in 1968. In 1983 he became Professor in the Department of Mathematics and Statistics.

He was president of the Canadian Mathematical Society from 1992 to 1994, received the Prize Urgel-Archambault of the ACFAS in 1995 for Physics, Mathematics and Engineering, was elected Fellow of the Royal Society of Canada (Academy of Sciences) in 1997, and was nominated Fellow of the John Simon Guggenheim Memorial Foundation in 2003. He served on many scientific and policy-making bodies such as NSERC (1982-86, 1996-99), Killam (1998-2001), National Defense (1989-1999), and National Steering Committee for Mathematics (2000-02), and is currently a member of the Synge Committee and the Fellowship Selection Committee of the Royal Sociey of Canada (2002-05).

2. Research interests

His research interests range over a very broad spectrum of subjects in Mathematics, Engineering, Sciences, and more recently in Medicine. His first contact with research goes back to the era of the first satellites when he was working as a summer student for the High Altitude Research Project at McGill University. Problems coming from the Space Industry were strong motivations for Numerical Analysis and the then young Control Theory.

In his thesis in 1970 he independently introduced the product space approach in the theory of delay-differential systems, followed in 1980 with A. Manitius by the structural operators which incorporate the specific delay structure of the system, and finally in 1987 with his Ph.D. student J. Karrakchou, he created a general framework to deal with large families of delay systems (retarded, neutral type delay differential equations, integro-differential equations, difference equations) including delays in observation and control all in a single product space framework with appropriate structural operators.

At the beginning of the eighties he became interested in Optimal Design problems of thermal diffusers and radiators for Canadian Communication satellites suggested by the Department of Communications and Spar Aerospace. In 1983-84 he became "Directeur de Recherches" at the Ecole des Mines and began a fruitful collaboration with Jean-Paul Zolésio. In 1989 he was awarded a 2-year Killam Fellowship for his project "Shape Analysis and Optimization". Over the years his interest shifted from purely numerical work to deeper theoretical issues. In that period the mathematical community made extraordinary advances to provide sound mathematical foundations to the field. In 2001 Delfour and Zolésio published a broad account of the theoretical foundations of shape and geometry in book form that received excellent reviews: "This is an outstanding book" (J. Sokolowski, AMS Math Reviews 2002). The book also contains many original contributions that had not been published elsewhere,

In the eighties Delfour also worked on the Control and Stabilization of large flexible space structures (MSAT) for the Canadian Space Program. Again applied and fundamental research are carried out in the form of contracts with the Communications Research Center in Ottawa and in the form of contributions to the mathematical control theory of partial differential equations such as the two-volume book by Bensoussan, Da Prato, Delfour and Mitter which also received exceptional reviews by I. Lasiecka (AMS Math Reviews). He also worked in Numerical Analysis where he introduced with W.W. Hager and F. Trochu in 1981 and with his Ph.D. student F. Dubeau in 1986 mesh-dependent discontinuous formulations of ordinary differential equations from which most one-step, multistep, and predictor-corrector approximation schemes can be recovered. The work was extended in 1998 to systems with impulses. This also led to high-order non-iterative schemes for the nonlinear matrix Riccatti differential equation in 1992.

The work on shape and geometry is quite fundamental with potential applications in many areas of sciences, engineering and medicine. For instance the results on the oriented distance function have been well received among experts in image processing and robotics. In the theory of thin and asymptotic shells, a completely intrinsic differential calculus on smooth sub-manifolds of co-dimension one was developed by a marriage of the notion of tangential derivative and the oriented distance function. It is also used to introduce an intrinsic characterization of Sobolev spaces on open domains in a C1,1 sub-manifold. This approach leads to significant simplifications in the associated calculus and functional analysis. As an illustration, he gave what seems to be the first completely intrinsic proof of Korn inequality in the C1,1 case which is a central part of the theory of thin and asymptotic shells. >From this Delfour obtained the thin and asymptotic models of shells without the classical mathematical and mechanical assumptions. Part of this work is now being translated in Russian. All this also applies to thin fluid shells such as oceans on the surface of the Earth.

Among his other interests, one could mention the management of nursing services for the Department of Social Affairs, the focusing of laser beams for Hydro-Quebec, the assignment of radio frequencies to land mobiles in large urban areas, and the Onchocercosis Control Program in West Africa to reduce the parasital disease whose ultimate stage is called the River Blindness. He was also the co-organizer with A. Bandrauk and C. Le Bris of a recent CRM Workshop on Quantum Control: mathematical and computational challenges in 2002.