Talks are Tuesdays at 4:00 and will be held in O'Connor 105 unless otherwise noted. There will be refreshments before all talks in O'Connor 31 starting around 3:30pm.

- Apr. 9
Ted Stanford, U.C. Berkeley
Title: n-triviality in knots, braids, and groups

"How many independent ways are there to undo a knot?" By "independent" I mean that a knot that is simultaneously undone in several independent ways stays undone and does not become knotted again. This notion can be made precise, and one defines an n-trivial knot to be a knot which can be undone in n+1 independent ways. I will discuss and illustrate several constructions of n-trivial knots. The obstructions to a knot being n-trivial are the recent knot invariants of Vassiliev (the ones of order less than or equal to n), which are closely related to the Jones polynomial and its generalizations. For any n, the set of knot types modulo n-triviality forms an abelian group. The notion of n-triviality can be extended to the braid groups and then to arbitrary groups, where it characterizes the nth group of the lower central series.

- Apr. 16
Steve Wilson, Sonoma State University
Title: Regular star polygons

We will define regular star polygons, see some applications to number theory, and analyze their compostion to obtain some graph theoretic results and measurement formulas.

- Apr. 23 Mary Cannell, George Green Memorial Fund
Title: George Green, Mathematician and Physicist 1793-1841: The background to his life and work

George Green was a miller, born in Nottingham in 1793. His contributions to mathematics and physics were considerable - not least Green's functions and Green's Theorem. The talk will centre on Green's life, his social and academic circumstances - which impeded the publication of his work, his time in Cambridge, his early death and subsequent neglect. It will conclude by tracing the events which have led to his recent recognition and acclaim, and which culminated in celebrations for the bicentenary of his birth and the dedication of a plaque in Westminster Abbey.

- Apr. 30 Jerry Alexanderson, Jean Pedersen and Hans Walser, SCU, SCU,
and ETH, Zuerich
Title: A medley of mathematical models

A relaxed demonstration of some mathematical models, including polyhedra that turn inside out, stick models that move in mysterious ways, and cardboard models that pop-up. Contributions from the audience will be welcome (we already know that Scott Johnson will bring at least one model he has invented).

- May 7 Eloise Hamann, San Jose State University
Title: An algebraist looks at the Jacobian conjecture

The Jacobian conjecture: If F is a map from C^n to C^n where F( (a_1, ... , a_n) ) = ( p_1(a_1, ... , a_n), ... , p_n(a_1, ... , a_n) ) where p_i are polynomials then if the Jacobian determinant is a non-zero constant, then F is invertible and F^-1 is a polynomial map. Equivalently C[p_1, ... , p_n] = C[x_1, ... x_n] where p_i are polynomials in { x_j }. The problem has been attacked using algebraic geometry, topology, differential equations, and graph theory. The talk will discuss an approach which uses commutative algebra and some history of the problem.

- May 14 Peter Hilton and Jean Pedersen, State Univ. of New York and SCU
Title: New wine in old bottles: Fibonacci and Lucas numbers revisited

Despite the remarkable longevity there are still many new results among the Fibonacci and Lucas numbers. We describe a few of our most recent discoveries.

- May 21 Paul Halmos, Santa Clara University
Title: My religion of mathematics

- May 28 Edward Dunne, Oklahoma State University
*(Recent addition)*Title: Pianos and Continued Fractions

It is an old problem in music that you cannot tune a piano perfectly. To understand why takes a little bit of physics and a little bit of elementary mathematics. Various methods of tuning have been used. The objective of each is to minimize in some way the amount the piano will be out of tune. Curiously enough, the modern solution to the problem is related to logarithms with a base of the twelfth root of two = 2^(1/12). A related problem is that of building a consistent scale based purely on acoustic principles. The talk will explain the problems and some of the solutions.

The prerequisites for the talk are a knowledge of fractions and an interest in music.

- June 4 Dennis Smolarski, Santa Clara University
Title: Linear systems, constrained spaces, projection solution methods

This talk will review projection methods for solving linear systems, and then discuss a strategy for adapting projection methods to solve constrained systems.

Anyone wishing further information about any of these talks should
contact the coordinator of the Colloquium Series, Prof. Ed Schaefer,
` eschaefer@scuacc.scu.edu
`