Santa Clara University

Mathematics and Computer Science department

SCU Mathematics/CS Colloquium Series

Fall 2009

All talks are Tuesdays at 4:00 pm in O'Connor 207, unless otherwise announced.

October 6:  Hongyun Wang, Dept. of Applied Mathematics and Statistics, UC Santa Cruz

Title: Mathematical studies of molecular motors

Abstract: Molecular motors are very small and operate in an environment dominated by high viscous friction and large thermal fluctuations. Because of their small size, molecular motors behave very differently from macroscopic motors.  

We introduce the mathematical governing equations for molecular motors and describe several of their peculiar behaviors. The goal is to understand single-molecule experimental data and to discover physical mechanisms from experimental data. For that purpose, we discuss two issues: the Stokes efficiency and the potential profile. The Stokes efficiency measures the "effectiveness" of a molecular motor in utilizing chemical energy to drive itself through viscous fluid. For molecular motors, the Stokes efficiency is different from the thermodynamic efficiency. The potential profile represents the motor driving force as a function of motor position. We discuss the mathematical framework and numerical methods for constructing motor potential profiles from time series of motor positions measured in single-molecule experiments.

October 13:  Estelle Basor, American Institute of Mathematics

Title: Eigenvalues of Toeplitz Matrices (This talk in O'Connor 110)




Abstract: Any square matrix with constant values along each diagonal is called a Toeplitz matrix. Toeplitz matrices arise in many areas of mathematics including analysis, probability theory, and mathematical physics. The goal of the talk will be to describe the limiting behavior of the eigenvalues as the size of the matrix grows. Many examples will be presented. Only a knowledge of basic linear algebra will be assumed.

October 20:  Shirley Yap, CSU East Bay

Title: Differential Equations---Not Just a Bag of Tricks!

Abstract: Differential Equations is often viewed as a subject full of tricks to solve specific kinds of problems, such as homogeneous and exact equations. However, there is a beautiful and powerful technique that unifies and extends many of the these techniques. The method, pioneered by Sophus Lie in the latter part of the 20th century, exploits the invariance of the equation under certain transformations in order to find a coordinate system for which the equation simplifies greatly. In addition to explaining the method and applying the method to several nonlinear ordinary differential equations, I will highlight the geometric nature of the symmetry method with many graphics and animations.

October 27:  David Czerwinski, San Jose State University

Title: The Math of Moneyball (and Airline Safety)

Abstract: The book Moneyball chronicles the 2002 season of the Oakland
A’s and highlights their use of quantitative methods. In this talk,
we show how the A’s effectively tied their strategic goals to simple
mathematical models. We take a look at the data that they based their
models on and update the story through the end of the 2007 season.
During the second half of the talk, we will show how one of the
methods used by the A’s can also be used to answer an important
question about airline safety: Are all US airlines equally safe?

 

November 3: Chris Goff, University of the Pacific

Title: Fusion Algebras and Accidental Trigonometry (or How I Spent My Sabbatical)

Abstract:  We discuss the notion of a fusion algebra, which neatly combines elements of abstract algebra with linear algebra.  In particular, I explain how the search for a specific fusion algebra led indirectly to the discovery of a cosine identity and its eventual proof.


November 10:Rob Beezer, University of Puget Sound

Title: An Introduction to Algebraic Graph Theory

Abstract: A graph is a set of "vertices" that can be joined by "edges."  The presence, or absence, of an edge between two vertices indicates a relationship between the vertices.  A very natural alternative to a graph is a matrix of zeros and ones, whose rows and columns are indexed by the vertices of the graph.  An entry equal to one in the matrix is equivalent to an edge, while a zero entry indicates no edge.

This matrix opens the possibility of using all of linear algebra to study graphs, and this is the theme of this talk.  We present several theorems that relate natural properties of graphs to natual properties of matrices, and vice versa.  We only assume a familiarity with basic linear algebra, such as matrix multiplication and eigenvalues.


November 17: TBA

December 1: Jared Maruskin, San Jose State University

Title: A Mathematical Introduction to Lagrangian and Hamiltonian Dynamics

Abstract: Everybody knows Newton's laws of mechanics: F = ma, that every action has an equal and opposite reaction, the inverse square law of gravitation. Not as many people, however, are familiar with the subtle and powerful abstraction of these laws known as Lagrangian and Hamiltonian Mechanics. These latter formalisms of mechanics combine the calculus of variations, advanced multivariate and vector calculus, and differential geometry, creating a powerful system of computation and elegant manifestation of the laws of nature. In this talk we will introduce some of the mathematics behind these theories and relay them to simple mechanical problems. Audience members should be familiar with multivariate/vector calculus and differential equations.

There will be refreshments before each talk in O'Connor 31 starting at 3:45pm.

 

If you have a disability and require a reasonable accommodation, please call/email Frank Farris 408-554-4430/ffarris at scu dot edu (or use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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