Mathematics Colloquia

Fall 2002

Sept. 27 (12 p.m., LA5-148) Louis Komzsik, CSULB.

Eigenvalues and Eigenvectors: What are They Good for and How to Find Them?

The talk starts with an elementary introduction to the geometric meaning of the eigenvalues and eigenvectors. The main numerical discussion focuses on the Lanczos method implementation and its practical use. Finally, real industrial applications from structural analysis in the automobile industry are shown, specifically normal modes, acoustic and brake analysis. The talk is suited to both an undergraduate audience and to graduate students or faculty members.

Oct. 4 (3 p.m., LA5-148) Masamichi Takesaki, UCLA.

Operator Algebras Around Us.

The talk is intended to introduce Operator Algebras in terms of every day language of mathematical community by showing that operator algebras appear in our vicinity rather often.

Oct. 11 (12 p.m., LA5-148) Francis Edward Su, Harvey Mudd College.

Simplicial Covers of High Dimensional Cubes.

Imagine a cube in 3-space and consider tetrahedra in it that are spanned by the vertices of the cube. How many such tetrahedra do you need to cover this cube? (The minimal triangulation is 5, but is the minimal cover a triangulation?) What about a cube in higher dimensions? For such a simple object, many things about cubes are not known. In this talk, we demonstrate new lower bounds for minimal covers of cubes that beat previous lower bounds of Smith(2000) in dimensions 4, 5, 6, 7, and 9.

Oct. 18 (12 p.m., LA5-148) Edray Goins, Caltech.

Icosahedral Q-Curve Extensions.

It is well-known that the roots of degree 5 polynomials cannot be expressed by radicals, but it is perhaps not as well-known that the roots can be expressed by points on elliptic curves. We present an overview of Felix Klein’s classical results, and give surprisingly simple formulas of such elliptic curves for classes of quintics first studied by Bring, Jerrard, and Euler.We assume the audience is familiar with basic properties of elliptic curves.

Oct. 25 (12 p.m., LA5-148) Wayne Dick, CSULB.

Teaching Induction to Algorithmists.

The first true programming language was predicate calculus. Lambda calculus followed shortly, and if user interface theory had stayed at that level, computer use would enjoy about the same general popularity as symbolic logic does today—not much. Difficult functions can be mastered by a wide population of people if the interface is reasonable and accessible. Is the same true of formal mathematics? While there may be no royal road to geometry as Euclid pointed out, there may be more or less accessible routes. This presentation will explore one such route for students of Computer Science who must learn induction to prove the validity of systems they create. I tailored a couple of induction theorems that use programming objects as the elements of an inductive argument. Being familiar and motivated, these programming objects provide an entry point for students in computer science to learn and apply induction in a meaningful and rigorous way.

Nov. 1 (12 p.m., LA5-148) Dave McKay, CSULB.

On Some Serious Issues Concerning Math and Physics Education at the University Level.

There is a widespread concern about the efficacy of the educational system. This talk will revisit some time-honored maxims of pedagogical wisdom and ask the key question: Do they work?

Nov. 8 (12 p.m., LA5-148) Al Sethuraman, CSU Northridge.

Determinantal Varieties.

This will be an elementary talk on a classical set of objects in Algebraic Geometry, namely, the varieties defined by the vanishing of the r by r minors of a generic m by n matrix. This is a very rich subject, and we will only give an overview of some of its features. We will end with some recent results of the speaker and his collaborator Tomaz Kosir on the variety of tangential curves over these classical objects.

Nov. 15 (12 p.m., LA5-148) Matt Foreman, UCI.

The Foundations of Mathematics.

The distinguishing feature of mathematics is that it is based on the notion of "proof". In a proof we are supposed to state all of our assumptions and then prove the consequences. We never do. How can we use some fact about geometry when proving something in algebra? Why can we use imaginary numbers to prove something about real numbers? How does mathematics fit together? What ARE the basic assumptions of mathematics? Can you prove every true mathematical fact? We discuss the answers to these questions.

Nov. 22 (12 p.m., LA5-148) Daphne Liu, CSULA.

From Channel Assignment Problem to the Lonely Runner Conjecture.

How do we assign TV channels validly (without interference) and economically (with the minimum span of channels used)? This talk begins with a graph coloring parameter motivated from this channel assignment problem (so called T-coloring). Then, we establish close connections among T-coloring and two number theory problems, one is about the density of integral sequences and the other is the parameter involved in the so called “lonely runner conjecture" (due to Wills in the 1950's). We show how to use these connections to solve some problems in graph theory and some problems in number theory.

Dec. 6 (12 p.m., ED1-040) Pedro Barquero, Santa Monica College.

Involutions, Quadratic Pairs and Clifford Structures.

We present the relatively new notion of a quadratic pair on a central simple algebra which is the twisted analogue of quadratic form in the same way thatinvolutions are twisted analogues of bilinear forms (up to scalar factor). The full force of this notion is in characteristic 2,as well as forthe definitions of Clifford groups and spin groups for central simple algebras with arbitrary involutions.

Unforeseen circumstances may affect this schedule; it is advisable to check with this web site to see if the particular talk you’re interested in is being given at the time, date, and location scheduled.