Australian Mathematical Society Web Site
Australian Mathematical Society Medal 1999
We are pleased to report that the winner of the 1999 Australian
Mathematical Society Medal is
Dr John Urbas of the Australian National University. The Society's
Medal is awarded annually
to a member of the Society for distinguished research in the
Mathematical Sciences. The
announcement of the award was made at the Annual Meeting of the
Society at the University
of Melbourne in July, where the meeting was run, for the first time,
in conjunction with the
American Mathernatical Society.
John currently lives in Canberra with his wife and three children.
Immediately after the medal presentation, John spoke to the Joint
Meeting about aspects of his research.
The citation for the award read:
John Ivan Evgen Urbas was born on 14 April 1959 in Cooma, New South
Wales. He studied at the Australian National University, receiving his B.Sc
with First Class
Honours in 1981 and his Ph.D. in 1985 under Professor Neil Trudinger.
He worked for a year at the Courant Institute in New York before
returning to the
Amstralian National University in 1986 to take up a prestigious Queen
Elizabeth II Fellowship. He was awarded an Alexander von Humbolt Research
Fellowship at the University of Bonn in 1996, where has also had several other
research visits. He
also spent six months at Northwestern University in 1989. He is
currently a Fellow at the CMA at ANU.
Dr Urbas is a leading international researcher in the Monge-Ampere
equation and
its associated mathematics (nonlinear partial difierential equations,
difierential geometry, convex analysis and measure theory).
His work utilizes a unique blend of
e
PDE, geometry and measure theory to tackle deep and technically
complex problems. He persistently works at big problems over
long periods. This staying power.
which received special note from his assessors, has been rewarded with
the production of major results that will remain as key milestones in the
literature. These include:
- Necessary and sufficient conditions for a convex hypersurface of
prescribed Gauss curvature to be a graph over a domain in n-space.
- A proof that convex graphs over convex domains, with smooth Gauss
curvature, vertical at their boundary, must be smooth manifolds with
boundary.
The analogous results for mean curvature were major
accomplishments in the
theory of minimal surfaces and geometric measure theory. The
Gauss curvature
case required completely different techniques. (Published
in J. Inst. Henri Poincare.)
- Positive resolution of the long-outstanding problem of global
reglarity of the natural boundary value problem for the Monge-Ampere equation.
This was
resolved independently by Caffarelli by different techniques.
Other significant contributions lie in curvature flow, oblique
boundary value problems,
interior regularity and extensions to more general equations.
All his assessors stressed his highest quality international standing
in his field. Their
comments included: "Urbas is one of the world masters in the field of
fully non linear elliptic equations".
"He has great imagination coupled with powerful analytic
technique (and) terrific geometric intuition. ... I am constantly
struck by his papers.
Each one has new ideas." "He never was looking for easy problems ...
but only for the
essential which turned out to be very difficult. I have great,
respect to such
personality, it is so hard t,o keep concentration on one particular
problem for years and finally to succeed."
Finally, paraphrasing an assessor: The Medal is a fitting recognition
of Dr Urbas'
contribution to the leadership that Australia holds in the theory of
fully nonlinear
equations and its applications, which is one of the most up to date
and promising
directions in modern Mathematics.
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Last update: 9/09/99