Santa Clara University

Mathematics and Computer Science department

SCU Mathematics/CS Colloquium Series

Fall 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 October 5, O'Connor 207

Speaker: Ken McLaughlin, University of Arizona and MSRI

Title: Random Matrices Beyond the Usual Universality Classes

Abstract: The statistical behavior of eigenvalues of large random matrices (i.e. in the limit when the matrix size tends to infinity) has been investigated extensively, for probability densities of the form C \exp{-Tr V(M)} where V(x) is a smooth, real valued function of the real variable x, and V(M) is defined on matrices by "the usual procedure". First goal: provide a background and introduction to the above.

But for probability densities in which the TRACE does not appear linearly, the situation is less understood. A simple example is: C \exp{ (Tr ( M^2))^2} (i.e. square the trace). Second goal: explain the source of the complication.

Third goal: Describe results. (Joint work with Misha Stepanov, Univ. of Arizona)

Tuesday October 19, O'Connor 207

Speaker: Wolfgang Polak, Computer Science Consultant

Title: Factoring on a Quantum Computer

Abstract: All practical public-key encryption systems rely on the complexity of either factoring or discrete logarithms. Both problems can be solved efficiently on a quantum computer. Thus, once built, quantum computers can defeat most known digital security schemes.

This talk introduces essential features of quantum mechanics needed to characterize quantum information, quantum state transformations and their use for computation. Peter Shor's polynomial-time factoring algorithm will be used to illustrate the unique features of quantum computation.

Tuesday October 26, O'Connor 207

Speaker: Ed Schaefer, Santa Clara University

Title: Continued Fractions

Abstract: An example of a finite continued fraction is 4+(1/(2+(1/(1+(1/(3+(1/7)))))), which equals 349/80. The numerators must always be 1. Infinite continued fractions continue forever, like 1+(1/(2+(1/(2+(1/(2+ …, which converges to sqrt(2). Continued fractions can be used to find very good rational approximations to real numbers. This gives them applications such as finding solutions to equations like x^2+dy^2=1 for a given d and in cryptography. In addition to presenting applications, we will present several theorems and give some fun examples. A high school degree is sufficient background for this talk.

Tuesday November 2, O'Connor 207

Speaker: Ellen Veomett, CSU East Bay

Title: From Spheres to Dots

Abstract: Say you are given a rubber band which is not rubbery at all; in fact, its length is fixed. You are asked to make a shape with the largest possible enclosed area. What kind of shape would you make? This question is an instance of an isoperimetric inequality. Given a fixed "perimeter", find the shape with the largest "area". In this talk, we will discuss a few very different types of isoperimetric inequalities. We will explore the Euclidean isoperimetric inequality, along with a clever proof of that inequality using the geometric Brunn-Minkowski Theorem. We will then consider a couple of isoperimetric questions in discrete spaces; one being the set of all integer points inside a box. Some of the shapes of the resulting sets of minimal boundary may surprise you!

Tuesday November 16, O'Connor 207

Speaker: Derek Purdy, BaroSense, Inc.

Title: Mathematics in Medical Device Research & Development

Abstract: Have you ever sat in a math class and wondered, when am I ever going to use this stuff?? This colloquium will explore the application of mathematics at start-up companies in the medical device industry. The use of math adds robustness to specification development and makes claims about data more credible. Math is useful in developing models to explain test results and also to predict future results. Perhaps most importantly, people who can understand, use, and explain mathematics to others in a friendly, non-condescending way are generally respected for it and are taken more seriously by their peers than those who cannot. Learn how you can be a leader in your field by applying what you already know! The branches of mathematics drawn upon for this discussion will include arithmetic and algebra, probability & statistics, and integral calculus.

If you have a disability and require a reasonable accommodation,
please call/email Rick Scott 408-554-4460/rscott at scu dot edu (or
use 1-800-735-2929 TTY—California Relay).

Abstracts of previous talks are available here.
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