Richard Palais
Adjunct Professor
Office: RH 410 H
In 1997, after 37 years as a member of the Brandeis
Department of Mathematics, I retired to leave myself more time to
work in the area of Mathematical Visualization and more specifically to
continue the development of my Macintosh program 3D-Filmstrip (now called 3D-XplorMath).
In the Fall of 2004, my wife, Chuu-lian
Terng, resigned from Northeastern Univ. to accept a position in the mathematics
department at UCI (where she holds
the Advance Chair) and we have now moved permanently to Irvine. I am continuing
to work on mathematical visualization and in particular I am cooperating
with David Eck of Hobart and William
Smith College, helping with the design of his Java port of 3D-XplorMath,
that will be called VMM---for The Virtual (or Visual) Mathematical Museum.
However I have also partially "unretired" and I am now an Adjunct
Professor of Mathematics at UCI, which means I will be teaching one
or two courses per year.
Teaching
Fall 2009
In the Fall Quarter of 2009 I will be teaching Math 218 (First
Year Graduate Topology).
Prospectus
for Math 218A.
Research
My Curriculum Vitae and Bibliography of
Published Works.
My long term research interests have
been in the areas of:
- Compact Differentiable Transformation Groups
- Nonlinear Global Analysis
- Critical Point Theory (in particular Morse Theory)
- Submanifold Geometry
- Integrable Systems and Solitons
My current research
In recent years I have been working on the theory of integrable,
one-dimensional wave equations---an area that is usually referred to as soliton
mathematics. I wrote an expository article
for the Bulletin of the AMS (October 1997 issue) called The
Symmetries of Solitons.
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The Breather
Pseudospherical Surface
(Produced using 3D-XplorMath)
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In recent years I have developed a strong interest in mathematical
visualization, and one of my major ongoing projects is the development
and continued improvement of a program called 3D-XplorMath for the
MacOS. This is a tool for aiding in the visualization of a wide variety
of mathematical objects and processes. Based on what I have learned
from my experience in writing this program, I wrote an essay called "The
Visualization of Mathematics: Towards a Mathematical Exploratorium" that
appeared in the June/July 1999 issue of the Notices of the American
Mathematical Society.
Here is a Gallery of
visualizations that were produced using 3D-XplorMath.
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Home |
Office |
| 45 Murasaki Street |
Department of Mathematics |
| Irvine, CA 92617-4088 |
103 MSTB UC Irvine |
| Mobile: 949 468 7102 |
Irvine, CA 92697-3875 |
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Voice: 949 824 3151 |
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Fax: 949 824 7993 |
Click here to
send me email at palais@uci.edu
Created: Dec 22, 2004 Last
Modified: Dec 22, 2004