Santa Clara University

Mathematics and Computer Science department

SCU Mathematics/CS Colloquium Series

Spring 2010

All talks will be at 3:50 PM.

There will be refreshments before each talk in O'Connor 31 at 3:40 PM.

Tuesday April 13, O'Connor 106

Speaker: David Mead. Professor Emeritus, U.C. Davis

Title: Powerful Triangle

Abstract: Simple proofs of an important mathematical result and a deep
topological theorem will be developed. Usually, for a Colloquium talk
a more detailed description is provided so that anyone who desires can
insure of having the necessary background. The speaker gives assurance
that everyone already has the required background.



Tuesday April 20, O'Connor 106

Speaker: Helen Moore, Pharsight

Title: Optimizing drug doses using differential equations Abstract: To
determine recommended drug doses, often the "guess and check" method
is used in clinical trials. This talk is about an alternative, which
uses mathematical models and techniques to predict optimal drug levels
before any testing takes place in patients. Starting from a simple
predator-prey system of differential equations, we will explore
mathematical disease models and predictions of optimal drug
concentrations using calculus of variations.


Tuesday April 27, O'Connor 106


Speaker: Molly Schatzel Title: Triangle Groups and Automaticity

Abstract: We consider the question of whether the greedy normal form
for a Coxeter group provides an automatic structure.  Such structures
are of interest because they allow one to automate computations in
infinite groups.  We will use an equivalent geometric formulation
called the "fellow traveler property" and include some colorful

May 4. No colloquium scheduled as of now.


Tuesday May 11, O'Connor 106


Speaker: Victor Garcia, Santa Clara University


Title: Patterns in Pascal's Triangle, Tetrahedron, and Simplex



We will discuss the trinomial and tetranomial analogues of known
results for binomial coefficients.  This will involve ideas from 2-,
3-, and 4-dimensional geometry.  Our particular interest has a strong
geometric flavor and we look for geometric configurations within
geometric figures, in each of these dimensions, that have very special
relationships to each other.  We will begin by recalling special
relationships among binomial coefficients and then investigate their
analogous results in higher dimensions.

A knowledge of high-school geometry and algebra is all this required
to understand this talk.


Tuesday May 18, Pi Mu Epsilon dinner


Thursday May 20, O'Connor 206


Speaker: Jessica Purcell, Brigham Young University


Title: The geometry of unknotting tunnels


In 3-manifolds, geometry and topology are very closely
related.  By the geometrization conjecture (now theorem), any
3-manifold decomposes into geometric pieces.  Thus in theory, we
should be able to use geometry to further understand and distinguish
3-manifolds described topologically.  However, relating topological
properties of a manifold to geometric ones seems to be difficult.  For
example, the complement of a knot in the 3-sphere often has a
topological description: a diagram, or graph with over/under crossing
information at each vertex.  Although knot complements have been known
to be geometric for three decades, we are still unable to answer very
basic questions about their geometry, such as estimating their volume
from a diagram, finding embedded geodesic surfaces, or even describing
explicit isotopy classes of geodesics.  In this talk, we will examine
the question of geodesics.  In some classes of knots, there is an
important (topological) arc embedded in the knot complement, called an
unknotting tunnel, whose complement is a handlebody, i.e. a solid
double torus.  In all known examples of hyperbolic knots, this
unknotting tunnel straightens to be a geodesic.  Is it always
geodesic?  We will investigate this question, and recent progress on
it and some of its generalizations.

Tuesday May 25, O'Connor 106


Speakers: Jean Pedersen and Victor Garcia, Santa Clara University


Title: Number tricks, puzzles, and mathematical oddities.



Victor Garcia will present, among other things, some of the number
tricks he created while doing summer research in 2009, and Jean
Pedersen will present some of the interesting puzzles, and
mathematical ideas, she encountered at the Gathering for Gardner
conference she attended at the end of March, 2010.

This colloquium will be an audience participation event and we
hope that everyone present will have a good time and learn
something fun, and maybe even useful, about mathematics.

If you have a disability and require a reasonable accommodation,
please call/email Dan Ostrov 408-554-4551/dostrov at scu dot edu (or
use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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