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).
