Fall 2004 Schedule of Speakers

 

Date	Location	Speaker	Topic
Thurs 11/18 @ 3:30pm	FN4	Alissa Crans, Loyola Marymount University	Quandles, Braids and Tangles, Oh My!  While it may sound surprising, algebra and topology actually have a very close relationship! One way to demonstrate this connection is through the language of quandles. A quandle is a set equipped with two binary operations which satisfy identities that are closely related to the properties satisfied by the operations of left and right conjugation. After examining examples of quandles, we will illustrate their connection to knot theory, and in particular, to the three Reidemeister moves. We will also explore the method which enables us to associate a quandle to a given knot. Finally, we will answer the question, ``Why should we even care about these things called quandles?"
Friday  11/12 @ 12:30pm	Johnson Hall, Room 201	Ron Buckmire, Occidental College	Different Differences.  From calculus we know that a derivative of a function can be approximated using a difference quotient. There are different forms of the difference quotient, such as the forward difference (most common), backward difference and centered difference. I will introduce and discuss "Mickens differences," which are decidedly different differences for approximating the derivatives in differential equations. Professor Ronald Mickens is an African-American Physics Professor at Clark Atlanta University who has written nearly 150 journal articles on this and related topics. These nonstandard finite differences can be used to produce discrete solutions to a wide variety of differential equations with improved accuracy over standard numerical approximation techniques. Applications drawn from first-semester Calculus to theoretical fluid dynamics will be given. Students are very welcome to attend. Knowledge of some elementary derivatives and Taylor approximation will be assumed.
Fri  10/29 @ 12:30pm	Johnson Hall, Room 201	Erica Flapan, Pomona College	The Shape of Space. We would like to understand the shape of our universe. People often assume that we live in R3, since it seems impossible to imagine any other possibility. In fact there are many other possibilities for our space, but we need to be able to visualize them. To help us with this task we first consider the analogous problem for 2-dimensional creatures living in a 2-dimensional universe. We present some possibilities for a 2-dimensional universe, and explain how 2-dimensional creatures could visualize them. Then using similar techniques we discuss possibilities for our own space and their characteristics. We conclude by explaining a recent model of our universe that is finite but has no boundary.
Fri 10/8 @ 12:30	Johnson Hall, Room 201	Francis Edward Su, Harvey Mudd College	Phylogenetic Tree Games. One big mathematical problem in biology is how to make sense of genomic data. For instance, given a set of DNA sequences, can we infer something about the relationships between the corresponding species? One way to represent those relationships is to construct a "phylogenetic tree", or a "tree of life". Understanding such trees is the starting point for a number of interesting questions in geometry, topology, algebra, analysis, combinatorics, statistics, and computer science. In this talk, I'll give an introduction to this area and a survey, and then describe some recent work of mine, joint with Claus-Jochen Haake and undergraduate Akemi Kashiwada '05, that relates cooperative game theory to phylogenetic trees.
Fri 10/1 @ 12:30	Johnson Hall, Room 201	Jennifer Quinn, Occidental College	Synchronicity: Alternating Sums, Determinants, and Exclusion. Identities involving sums of alternating terms are frequently tackled using the Principle of Inclusion-Exclusion. While a powerful tool, it has a tendency to obscure any relationship among the sets being considered. My goal is to directly understand the identities by finding a correspondence between odd and even sets. Coincidentally, a colleague asked me about calculating a particular determinant combinatorially. When the answer ended up being related to the alternating identities I was investigating, I was stunned. The coincidence was to great to be ignored. So just was is the connection between determinants, alternating sums, and the Principle of Inclusion-Exclusion? Come and find out.