Dr. Peter Lax's Lectures

The Computation of Compressible Flows
Monday, November 15, at 1:15pm, in 499 DSL (refreshments to be served at 12:45 pm)

Abstract: In the last 50 years mathematicians, physicists and engineers have devoted much effort to the computation of flows of compressible gas that are of theoretical or practical interest.This is a challenging problem, for such flows inevitably contain shocks.In this talk I will describe an approach taken by Z D Liu and the speaker that exploits the symmetric nature of the equations governing compressible flow, and give some examples of successful computations.

This talk is meant for those interested in computational fluid dynamics.
The Paradox of Education - PUBLIC LECTURE
Wednesday, November 17, 4:00pm, in Werkmeister Reading room - 116 Dodd Hall (refreshments to be served at 3:30 pm).

Parking will be available beginning at 3:00 p.m. on November17. The lot is located at the corner of Pensacola and Copeland Streets (entering the lot off of Pensacola Street, which is a one-way street).

Abstract: The paradox is that science and mathematics are developing with leaps and bounds at more than exponential rate. Does that mean that what we teach in high school and college is falling behind by leaps and bounds? Not necessarily; for, as Hilbert had observed, new discoveries bring simpler methods and new points of view which replace the older, more cumbersome ones.This is equally true in mathematical education; I will illustrate this with many examples in algebra and geometry.

The basic sciences, physics, chemistry, biology have revised drastically their high school and college curricula. We mathematicians should follow their example.
Degenerate Symmetric Matrices
Friday, November 19, at 3:30 pm, in 101 LOV

Abstract: A real symmetric matrix is called degenerate by physicists if it has a multiple eigenvalue. Wigner and von Neumann have shown long ago that the degenerate matrices form a variety of codimension two in the space of all real symmetric matrices. This explains the phenomenon of "avoidance of crossing" in one-parameter families of symmetric matrices.On the other hand degeneration is characterized by the vanishing of the discriminant; this is a single equation for the entries of the matrix. In this talk I investigate the representation of the discriminant as a sum of squares.

In the second part of the talk I show that some two-parameter linear families of real symmetric matrices always contain a degenerate one. This result is of importance in optics and other branches of mathematical physics.

This talk is meant for a general mathematical audience; no special knowledge is required.

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