|
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
||
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
|
 |
|
Professor Karen K. Uhlenbeck
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. `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
`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. '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.
|
|