Math

Mathematics Colloquium Abstracts, 2009-2010

Previous Abstracts

2008-2009      2007-2008      2006-2007

  Fall 2009 Abstracts

Tuesday, September 8, 4:00pm

Prof. Virgil Pierce, University of Texas - Pan American
Ford 201

Enumeration of Polygon Dissections

The Euler polygon division problem poses the question:  In how many ways may a (n+2)-sided polygon be divided into triangles whose sides are the sides and diagonals of the original polygon?  The solution is given by the Catalan numbers, which also solve such enumerative problems as:  the number of Dyck paths starting and ending at the x-axis, the number of ways a 2n-sided polygon can be glued together to give a sphere, and many others (perhaps most interestingly it has recently been shown that the Catalan numbers give the number of non-interacting solitary wave solutions to a 2D shallow water wave equation).  We will consider such generalizations as:  In how many ways may a  (2 n + 2)-sided polygon be divided into squares?  or In how many ways may a sphere or torus may be divided into pentagons?   This talk will be enjoyable for students with a general interest in Math and Science. 

Thursday, September 24, 4:00pm

Christina Edholm, Willamette University

Zero Forcing on a Graph

The zero forcing number of a simple graph G is defined as the smallest size of a zero forcing set of G.  We will discuss the properties of the zero forcing number of simple graphs and their subgraphs resulting from the removal of a single vertex or edge. In particular, we present results of zero forcing numbers for super triangles, grid graphs, and triangular grid graphs.

Friday, October 2, 2009, 3:00pm

Charley Mathes, Willamette University Student

Ropelength of Alternating, Almost-Alternating, and Paired Links

Charley Mathes will present his Summer Research from California State University/San Bernadino REU:
For any given link conformation L, which admits an alternating, almost-alternating or paired projection, we establish that there is a linear lower bound on the ropelength in terms of bridge number for the paired links and crossing number for the alternating and almost-alternating links.

Friday, October 9, 2009, 3:00pm

Mohan Rajagopalan, Loose Cannon Studios

What Every Student Should Know About Making Games 

It's common knowledge that game studios want their engineers to have strong math and computer science backgrounds. But what does that really mean? What, from a college math and computer science curriculum, does game development really leverage? This lecture takes a practical look at what skills are most valued in game development, with a particular emphasis on engineers just starting their careers in game development.

Thursday, October 15, 2009

Yevgeniy Kovchegov, Oregon State University

On MCMC and Mixing Rates

Markov Chain Monte Carlo (MCMC) is a method to simulate a desired probability distribution via constructing a Markov chain whose stationary distribution is the one we need. Mixing time describes the rate of convergence of a Markov chain to its stationary distribution. We will give examples of Gibbs sampling algorithms (also known as Glauber Dynamics). We will explain how strong stationary time and coupling are used to obtain bounds on mixing time. We will also discuss new approaches to coupling method and their applications.

Thursday, October 29, 2009

Andrea Walker, Sandia National Labs (and '08 Alum, Willamette University)

A Brief Intro to Cryptography and Related Job
Opportunities at Sandia Labs 

Andrea Walker will discuss summer intern opportunities in the fields of computer science, math, and engineering at Sandia National Laboratories, a science and engineering lab in Albuquerque, NM.
As a cryptographic mathematician for Sandia's cyber and information security department, Andrea's focus will be job opportunities in cyber security, specifically the Center for Cyber Defenders student internship program. She will also discuss the cryptography department in detail along with the type of work done within the department. Andrew will also give a technical presentation on cryptography including a discussion on cryptographic schemes, public key vs. private key, protocols, history, where public key crypto is headed, and a detailed description of Diffie-Hellman key exchange.
This presentation assumes an undergraduate level math or computer science education with no cryptography background.

In addition, Andrea will be available from 12:30-1:30pm in the Math Hearth to talk about Sandia internships, take resumes and conduct interviews. She is currently looking for students with backgrounds in math, physics, engineering and computer science (especially computer science). This is a wonderful opportunity for anyone interested in working at a national laboratory or learning more about applications of these fields.

Thursday, November 5, 2009

Prof. Chris Sinclair, University of Oregon

The Geometry of Polynomials With All Roots on the Unit Circle 

Coefficient vectors of polynomials with all roots on the unit circle exhibit an amazing amount of geometric structure. In this talk we'll look at the set of all coefficient vectors of all polynomials with all roots on the unit circle for fixed degree.  The symmetries, volume and structure based on the multiplicities of the roots will be explored. In addition, we'll look at several, easy to check conditions which guarantee that all roots of a given polynomial lie on the unit circle.

Thursday, November 12, 2009

Prof. Emeritus Richard Iltis, Wilamette University

Fourier Analysis: Some History an an Introduction 

In 1822, Joseph Fourier wrote a treatise studying the flow of heat using a differential equation. For a solution he expanded a function in a series of sines and cosines, and so began a branch of mathematics, Fourier Analysis. We will look at Fourier's work and some following developments.

Thursday, November 19, 2009

Spring 2010 Math Courses Preview

This week's Math Colloquium will be a preview of upcoming advanced math courses offered by the department. Come for a sneak peek before you set your spring class schedule; or if you already know what classes you're taking, stop by to learn about a variety of topics you may want to investigate further. New courses we'll preview are:

Number Theory
Combinatorics
Real Analysis
Senior Seminar: Cryptology
Senior Seminar: Markov Chains

Come for the Root Beer Floats; stay for the mathy goodness!!

Spring Abstracts