I am now Professor Emeritus at Brandeis.

After 37 years in the in the Brandeis Department of Mathematics, in 1997 I retired to have more time to work in the area of Mathematical Visualization, and more specifically to develop 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 the University of California at Irvine (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, which will be called VMM---for The Virtual (or Visual) Mathematical Museum. However I have also partially "unretired" and accepted a position as Adjunct Professor of Mathematics at UCI, which means I will be teaching one or two courses per year.

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

In recent years I have become interested in mathematical visualization, and one of my major ongoing projects is the development and continued improvement of a program called 3D-XplorMath for MacOS X. 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. With the help of Xah Lee, I have created a Gallery of visualizations produced using 3D-XplorMath.

I have also recently been thinking about 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.

Here is a link to my book The Geometrization of Physics,

And here is a link to Critical Point Theory and Submanifold Geometry, Lecture Notes in Mathematics #1353,Springer-Verlag, NY, jointly authored by me and Chuu-lian Terng.

My Curriculum Vitae and Bibliography of Published Works.