Lonseth and Milne lectures

Milne Lectures

Lonseth Lectures:

• May 27, 2008 at 16:00, in LaSells Stewart Center: (Lonseth Lecture) John Lee, Weierstrass Approximation Theorems

  Weierstrass published his celebrated approximation theorems in July of 1885. I will start with brief speculations on the antecedents of Weierstrass' work and move on to a selective survey of results and/or proofs related to Weierstrass' original theorems. The survey will include results and/or proofs of Lebesgue, Landau, de la Vallee Poussin, Bernstein, Korovkin, and Stone, as time permits.

• May 8, 2007 at 15:30, in LaSells Stewart Center: (Lonseth Lecture) Professor Jim Douglas, Jr., Purdue University, The Role of Capillarity in Multiphase Flow in Porous Media

  Professor Lonseth was very interested in seeing that mathematics interact with other disciplines to improve the understanding of phenomena in these disciplines, and this lecture will be devoted to showing by three examples the importance of including the effects of capillarity in approximating multiphase flows in porous media. The first example involves a simple laboratory experiment and was responsible for reorienting an experimental procedure in a major petroleum research laboratory. The second relates to the mathematical description of multiphase flow in fractured media, where omitting capillarity leads to a seriously incorrect model. The third example, which concerns three-phase flow, exhibits a nonstandard shock that is incorrectly simulated (or not found) without capillarity. The presentation will not require expertise in simulating flows in porous media.

• May 2, 2006 at 14:00, in LaSells Stewart Center: (Lonseth Lecture) Professor Peter Lax, Degenerate Symmetric Matrices

  A 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 symmetric matrices.This explains the phenomenon of "avoidance of crossing".
  Degenerate matrices S are characterised by the single equation discr(S)=0, where discr(S) is the discriminant of S. In this talk we investigate the nature of the discriminant, especially its representation as a sum of squares.
  In the first part of the talk it will be shown that if A,B,C are nXn symmetric matrices, and n is congruent 2 mod 4, there always exist three real numbers a,b,c, not all zero, such that aA+bB+cC is degenerate. This has interesting applications to symmetric hyperbolic systems of PDE-s, such as the equations of crystal optics.

• May 10, 2005 at 14:00, in LaSells Stewart Center: (Lonseth Lecture) Doug Arnold, Institute for Mathematics and its Applications, University of Minnesota, The New Mathematical Gravitational Astronomy

  Contemporary understanding of the cosmos is based on on Einstein's amazing insight that gravity is simply a manifestation of curvature. One ineluctable, though subtle, consequence of this theory of general relativity, is that violent cosmic events--imagine two black holes wildly orbiting around each other in the moments before they merge--emit gravitational signals that propagate off into space. The nascent field of gravitational astronomy seeks to use these tiny ripples on surface of spacetime as our first window to the universe looking outside of the electromagnetic spectrum. The technological and scientific challenges of detecting gravity waves are immense, but the mathematical difficulties which must to be overcome to interpret these signals through computer simulation of general relativity may be the greatest of all. This lecture, held during the centenary of Einstein's annus mirabilis and on the heels of 2005 Mathematics Awareness Month dedicated to the theme Mathematics and the Cosmos, will discuss the fascinating emerging science of gravitational astronomy and the mathematics and mathematical challenges at its heart.

• May 11, 2004: (Lonseth Lecture) Steven G. Krantz, Washington University in St. Louis, A Matter of Gravity

  It is a standard topic in any multivariable calculus course to develop the concept of "centroid" or "center of gravity", and to teach the student to calculate this center. Rarely is there any further investigation into properties of the center of gravity. Nonetheless, there are interesting questions about the center of gravity that could have been asked three hundred years ago, but evidently were not addressed until recently. We consider some new features and properties of the concept of center of gravity. Both topological and geometrical aspects will be examined. Stability results are proved.

• Apr 29, 2003: (Lonseth Lecture) John H. Ewing, Executive Director American Mathematical Society, The Mathematics Inside Your Computer

  Computers don't operate using only bits and bytes to perform logic and arithmetic. They use sophisticated mathematics to perform many of the routine tasks you take for granted every time you turn on your machine. This talk will survey a small sample of that sophisticated mathematics, from an unsophisticated point of view.

• May 28, 2002: (Lonseth Lecture) Colin Adams, Williams College, Real Estate in Hyperbolic Space: Investment Opportunities for the New Millennium

  Have you found the new investment climate a bit on the chilly side? Nervous about stocks, bonds and mutual funds? Afraid of risky investments in Euclidean space? Then real estate in hyperbolic space is for you. We will discuss the enormous potential of this new investment opportunity and describe the many fascinating properties of hyperbolic space that make it such an attractive place to live. This is the financial equivalent of the 1980's junk bond. Don't miss it. Bring your checkbook and credit references! No previous math or real estate background assumed! Recommended for students and faculty alike! Roger Ebert says, "Two fingers up!"

• May 22, 2001: (Lonseth Lecture) Douglas Lind, University of Washington, The Mathematics of Compact Discs

  How do compact discs record Beethoven symphonies, pictures, and computer programs? Why don't fingerprints or scratches seem to matter? What mathematics underlies this remarkable invention? I'll describe the surprising answers, which involve dynamical systems and error-correcting codes. You'll also learn why you should always clean your CD's by wiping them radially rather than with a more natural circular motion.

• May 16, 2000: (Lonseth Lecture) Constance Reid, Noted Mathematical Historian and Biographer, The Improbable Life of Richard Courant

  Almost thirty years after his death, Richard Courant remains a highly controversial figure in mathematics, complex and contradictory; but the message he emphasized throughout his long career was one that he had absorbed in his youth in Gottingen from David Hilbert and Felix Klein--the underlying unity of all the mathematical sciences, pure and applied.

• May 18, 1999: (Lonseth Lecture) Kenneth A. Ross, University of Oregon, "The Mathematics of Card Shuffling"

  How many times do you have to shuffle a deck of cards before it is well mixed? What do we mean by well mixed? Questions like this will be discussed and seen to lead to the study of random walks on certain finite groups. This is an expository talk on work by Persi Diaconis and his colleagues, though a colleague of mine and I have obtained some related but more technical results.

• May 5, 1998: (Lonseth Lecture) Philip A. Anselone, Oregon State University, The Power of Calculus: The legacy of Newton

  Isaac Newton developed calculus and used it to derive universal laws of motion and gravitation that apply not only on Earth but also to the planets and stars. His laws justify and explain the pervious discoveries of Galileo and Kepler. Newton's laws, particularly force equals mass times acceleration and the universal law of gravitation, are introduced in calculus classes, but usually there isn't enough time to deal adequately with their all-important consequences. The result is that students do not fully appreciate the extraordinary magnitude of Newton's accomplishments. In this lecture we shall discuss three topics that stem directly from Newton's laws: 1. Escape velocity of a projectile launched from the Earth; 2. The derivation of Kepler's laws of planetary motion; 3. The representation of solid bodies as point masses. Even today some of the details of Newton's analysis have to be sketched in order to make the arguments reasonably accessible to calculus students.

• May 6, 1997: (Lonseth Lecture) Margaret Wright, Bell Laboratories, Lucent Technologies, Model, Speed up, Optimize, Remodel: Fun and Profit for Mathematics and It's Friends

  Mathematics plays a major role in formulating and modeling real-world problems--but models are never right the first time. So mathematics also enters in speeding up complicated calculations, optimizing whatever the current model may be, figuring out its defects, and then producing a more realistic model. This talk will describe how mathematicians and computer scientists have worked with experts in radio engineering and user interface design to produce not only a useful product for Lucent Technologies (a software tool for designing wireless communication systems), but also original mathematical research in optimization and computational geometry.

• May 7, 1996: (Lonseth Lecture) Robert Osserman, Stanford University, The Shape of the Universe

  There are a few occasions in history when human beings are called upon to make a radical shift in the way they view their world. One such occasion dates back to ancient Greece when it was first understood that the Earth is not flat, as it appears, but is shpaed like a giant ball. We are now at another great turning point in human understanding when for the first time we are able to meaningfully pose and partially answer the question, "What is the ahspe of the entire unvierse?" The aim of the talk is to provide the background needed to understand both the question and its answers.

• May 25, 1995: (Lonseth Lecture) Ronald L. Graham, AT&T Bell Labs, Mathematics and Computers: Recent Successes and insurmountable Challenges

  There is no question that the recent advent of the modern computer has had a dramatic impact on what mathematicians do and how they do it. However, there is increasing belief that many apparently simple problems may in fact be forever beyond any conceivable computer approach. In the talk I will describe a variety of mathematical problems in which computers either have had, may have or will probably never have a significant role in their solutions.

• May 24, 1994: (Lonseth Lecture) Tsit-Yuen Lam, University of California-Berkeley, Mistakes We all Made: How Error-Free is Mathematics?

  Mathematics, as a subject, derives its beauty from its internal consistency and sound logic. It is thus axiomatic that the proofs and argumentations used in the development of mathematics be absolutely accurate and error-free. Yet the history of mathematics is replete with instances of false starts, half-truths, and incomplete or downright erroneous arguments. Even the greatest of mathematicians are known to have erred in their proofs. In the talk, Professor Lam will give a light-hearted view of some of the famous (or infamous) errors made in the long history of mathematics. Along the way, he will also comment on the pedagogical values of mistakes in mathematics, and discuss ways by which we may try to minimize our mistakes.

• Apr 27, 1993: (Lonseth Lecture) Mary Ellen Rudin, University of Wisconsin-Madison, Dimension

  When dealing with topological spaces which are note necessarily metric, we run into a variety of questions. We will discuss several rather nice classes of such spaces as well as some conjectures. We will prove, with the aid of one rather special example, that three of the conjectures are false.

• May 19, 1992: (Lonseth Lecture) John Horton Conway, Princeton University, On the Shape of Things

  Conway is recognized for his studies in combinatorics and group theory, which is the branch of algebra that studies the properties of symmetries of figures, and how you can go from one symmetry to another. Conway has made some major an fundamental discoveries in this field.

• May 14, 1991: (Lonseth Lecture) Ian Stewart, University of Warwick, Four Encounters With Sierpinski's Gasket

  Sierpinski's gasket is a fractal, obtained by repeatedly deleting the middle section of a triangle. It shows up in a number of different areas of mathematics, with surprising cross-connections. The talk will describe four occurrences of the gasket: 1. What Sierpinski originally invented it for; 2. Parity of binomial coefficients; 3. The Tower of Hanoi puzzle; 4. Michael Barnsley's Chaos Game.

• May 1, 1990: (Lonseth Lecture) Serg Lang, Yale University, A B C Conjecture

  Recently, there have been some deep new insights into classical old problems, like Fermat's last theorem. Some of these insights can be expressed in terms of fairly elementary mathematics involving polynomials and numbers. I will describe some of these insights.

• May 16, 1989: (Lonseth Lecture) George Andrews, Pennsylvania State University, Ramanujan's Lost Notebook

  The "Lost" Notebook provides us with a record (probably incomplete) of Ramanujan's discoveries during the last year of his life. A number of his formulas from this document have been proved and analyzed; however, many remain unproved and totally mysterious. We shall survey some of the topics covered by the "Lost" Notebook, and we shall consider some of those formulas which are still open.

• May 17, 1988: (Lonseth Lecture) G. D. Chakerian, University of California-Davis, Cantor Dust Under a Binary Tree

  This lecture will deal with some of the more paradoxical properties of the real numbers, from a geometrical point of view. In particular, the famous Cantor ternary set will be used to illustrate the idea of a fractal, a set of fractional dimension.

• May 19, 1987: (Lonseth Lecture) Gilbert Strang, MIT, Chaos: Strange Attractors and Fractuals

  Professor Strang is noted for his illuminating lectures on a wide variety of mathematical topics. His talk should appeal to students and former students of mathematics and also to teachers of mathematics from high school through graduate school.

• May 20, 1986: (Lonseth Lecture) Ivan Niven, University of Oregon, Some Surprising Results in Elementary Mathematics

  Although the background assumed is modest, the results are ingenious and not widely known. Professor Niven is noted for his lucid presentations of mathematical ideas. His lecture should appeal to students and former students of mathematics and also to teachers of mathematics from high school through graduate school.