Richard Palais' Research

University of California, Irvine
Department of Mathematics
340 Rowland Hall
Irvine, CA 92697-3875

Office Location: Suite 410 Office H Rowland Hall

Email: palais@uci.edu

Tel: (949) 468 7102 (mobile)

 

My Curriculum Vitae and Bibliography of Published Works.

Here is a list of my PhD students.

My long term research interests have been in the areas of:

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.

3D-XplorMath

The Breather Pseudospherical Surface    

(Produced using 3D-XplorMath)    

I have developed a long term interest in mathematical visualization, and one of my major ongoing projects has been leading an international team of mathematicians (callled the 3DXM Consortium) in the the development and continued improvement of a program called 3D-XplorMath. 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 the Home Page for 3D-XplorMath. You can download it and learn all about it there.

And here is a Gallery of visualizations that were produced using 3D-XplorMath.

In 2006, graphic artist Luc Benard and I entered a visualization of five mathematical surfaces into the NSF/Science Magazine Visualization Challenge, where it won First Prize and became the cover for the September 22, 2006 issue of Science.

Here is a movie of an invited presentation that Luc and I gave at Rochester Institute of Technology that gives the story behind the creation of the winning illustration.

Created:  Dec 22, 2008