Academic Excellence Visiting Scholar

Posted December 17, 2007

Last modified January 12, 2008

Paul Rabinowitz, University of Wisconsin
E.B. Van Vleck Professor of Mathematics
National Academy Member
1998 George David Birkhoff Prize in Applied Mathematics

Towards an Aubry - Mather type theory for PDE's

An abstract is available here.

Academic Excellence Visiting Scholar

Posted December 17, 2007

Last modified January 12, 2008

Paul Rabinowitz, University of Wisconsin
E.B. Van Vleck Professor of Mathematics
National Academy Member
1998 George David Birkhoff Prize in Applied Mathematics

Towards an Aubry - Mather type theory for PDE's

An abstract is available here.

Academic Excellence Visiting Scholar

Posted December 17, 2007

Last modified January 12, 2008

Paul Rabinowitz, University of Wisconsin
E.B. Van Vleck Professor of Mathematics
National Academy Member
1998 George David Birkhoff Prize in Applied Mathematics

Towards an Aubry - Mather type theory for PDE's

An abstract is available here.

Academic Excellence Visiting Scholar

Posted January 31, 2008

Last modified February 9, 2008

Richard A. Askey, University of Wisconsin
Member of the National Academy of Sciences

Binomial theorem, gamma and beta functions and extensions

The binomial theorem goes back centuries, yet there are

still interesting things one can do with it and extensions which

were found not that long ago which are very important. The gamma

and beta functions are not as old, a bit under 300 years.

There are important extension of them which have been found

much more recently, both in one and in several variables. Some of

these results will be described, proven, and/or used.

Academic Excellence Visiting Scholar

Posted January 31, 2008

Last modified February 11, 2008

Richard A. Askey, University of Wisconsin
Member of the National Academy of Sciences

What is Ptolemy's theorem and why is it useful to know a few different ways to prove it?

This talk will be accessible to all undergraduate math majors and any students who had a good high school geometry course.

Ptolemy was best known for his astronomy work, but his book on this contains an important theorem in geometry which is still of interest. The theorem deals with quadrilaterals inscribed in a circle, and was important to Ptolemy as a tool to construct what we would call tables of values of trigonometric functions. We know better ways to do that now, but Ptolemy's theorem is still important, both as a way of learning important ways of attacking some geometry problems, and because of other uses of it. A number of proofs will be given, including Ptolemy's geometric proof, Euler's proof using the law of cosines, a combination of these two proofs to extend Ptolemy's theorem to general quadrilaterals, and ways to reduce this problem to a simple problem on a line.

Academic Excellence Visiting Scholar

Posted January 31, 2008

Last modified February 9, 2008

Richard A. Askey, University of Wisconsin
Member of the National Academy of Sciences

Orthogonal polynomials &mdash what are they and some of the things one can do with them

Most of you know the names of some of the important classical orthogonal polynomials, Hermite polynomials, Legendre polynomials, and Chebyshev polynomials, and may even know some places where these polynomials arise. There are a number of other classical type orthogonal polynomials which will be discussed. The problems they arise in range from stable distribution of charges on an interval, which is connected eventually with Selberg's multidimensional beta integral, to the Rogers-Ramanujan identities, which themselves show up in statistical mechanics and other unlikely places in addition to their interpretation as partition identities for special classes of integers.

Academic Excellence Visiting Scholar

Posted March 1, 2008

Last modified March 3, 2008

Hyman Bass, University of Michigan
National Medal of Science Laureate (2006)

Improving U.S. Mathematics Education: Myths and Realities

Professor Bass has chaired the Mathematical Sciences Education Board at the National Academy of Sciences and the Committee on Education of the American Mathematical Society. Abstract of the talk: Although there is widespread dissatisfaction with U.S. students' mathematical performance, there is little agreement on the roots of the problem or its solutions. This presentation will argue that teacher capacity and teaching quality are key to the improvement of mathematics education, and will analyze the levers that could make a difference for their effectiveness.

Academic Excellence Visiting Scholar

Posted February 29, 2008

Last modified March 3, 2008

Hyman Bass, University of Michigan
National Medal of Science Laureate (2006)

Revisiting an approach to the two-dimensional Jacobian Conjecture

This is about an approach I tried many years ago using the Weyl Algebra. While I wasn't able to push it all the way through, it did make some interesting contact with diophantine geometry and classical function theory. Since no significant recent progress has been made on the Jacobian Conjecture, I thought that I might try to revive awareness of this approach. The Jacobian Conjecture is of broad mathematical interest.

Academic Excellence Visiting Scholar

Posted February 29, 2008

Last modified March 3, 2008

Hyman Bass, University of Michigan
National Medal of Science Laureate (2006)

Cake sharing, Euclidean algorithm, and square tiling of rectangles"

This talk will be accessible to all undergraduate math majors.

This talk answers the question: If you want to equally share c cakes
among s students, what is the smallest number of cake pieces
required? It makes interesting connections with all the topics in
the title.