Professor Karen K. Uhlenbeck
Sid W. Richardson Regents Professor of Mathematics
University of Texas, Austin
Physics, Room 202
Professor Karen Uhlenbeck made pioneering contributions to global geometry and gauge theory that resulted in advances in mathematical physics and the theory of partial differential equations. She has received numerous awards and honors for her mathematical work, including election to the National Academy of Sciences and the American Academy of Arts and Sciences. She received the MacArthur Prize in 1983, and was chosen as a plenary speaker at the International Congress of Mathematicians in Kyoto in 1990. In December 2000, she was awarded the National Medal of Science, the nation's highest scientific honor.
Geometry Across Three Centuries
April 10-12, 2001
Any student who has taken calculus knows, although perhaps is not impressed by, two important facts about mathematics. First of all, many of the important ideas in mathematics are very old. For example, calculus was developed by Newton, Leibnitz and Descartes a long, long time ago. Secondly, while it is important that mathematics is a necessary tool with applications in many disciplines, conversely, the ideas of mathematics itself have many sources. Sciences create mathematics by translating physical ideas into mathematical questions and equations. What is not so evident is that many of the old ideas are still connected with core research mathematics. Moreover, the process of developing new mathematics from other sciences is still taking place today. We illustrate this process with three centuries of examples of geometric equations.
Tuesday, April 10, 2001, 4:00 p.m. Physics Building, Room 202
"A selection of equations from nineteenth century geometry'"
We will look at a selection of equations like the Kortweg-de Vries Equation, the minimal surface equation and the Sine Gordon equation. Try to imagine how the nineteenth century mathematicians thought about them. How do they appear in modern mathematics
Wednesday, April 11, 2001, 4:00 p.m. Boyd Graduate Studies Research Center, Room 328
"Minimal surfaces and their uses"
There are many important sources of geometry in the twentieth century, such as Einstein's theory of relativity, minimization problems and high energy physics. We will emphasize some of the applications of minimal surfaces and the different mathematical objects related to them.
Thursday, April 12, 2001, 4:00 p.m. Boyd Graduate Studies Research Center, Room 328
"A glimpse into the future'"
In the twenty-first century, the impact of physics is still important and we will talk about the new concept of special Lagrangian three-folds which is in its infancy. However, most geometers believe that in the twenty-first century ideas from biology will become increasingly important. There are some pretty crazy minimization problems which come from trying to understand how DNA is cut and packed which are well worth musing on.