## Colloquium and Seminar Schedule

Spring 2011The Department is sponsoring or co-sponsoring several colloquia and seminars this term as listed below. Click here for information about the next scheduled talk. Check this page regularly for the latest schedule as more talks are added.

## February 2011

Wide World of Mathematical Biology

Speaker: Dr. Jonathan Forde

Wednesday, February 9th at 4:00pm

Room: Gulick 206A

(Refreshments will be served beforehand)

Abstract:

After a brief introduction to what mathematical biology is and why it is a growing area of active research, Forde will present preliminary results from some of his current research projects: immune therapy for HIV, treatment of hepatitis delta virus and the ecology of plant-herbivore-carnivore systems. He will also give a preview of the upcoming summer research program on modeling infectious disease.

Discovering the missing piece: 4-connected, 4-regular, claw-free graphs of odd order

Speakers: Trevor Gionet '12 and Yixiao Sha '12

Tuesday, February 22 at 4:45pm

Room: Napier 201

(Refreshments will be served beforehand.)

Abstract:

In 1995, Plummer published a paper in which he gave a characterization of the 4-regular, 4-connected, claw-free graphs. Based on that work, he and Hartnell published a paper on 4-connected, claw-free, well-covered graphs a year later. However, in his 1995 paper, Plummer inadvertently omitted some of the graphs with odd order. Last summer Trevor and Yixiao were working on a related question under the direction of Prof. Erika King when they discovered this omission. Together they completed Plummer's characterization of all 4-connected, 4-regular, claw-free graphs, and then showed the implications this has on the well-covered graphs he and Hartnell determined. In addition, they characterized the 4-connected, 4-regular, claw-free, well-dominated graphs. The talk will be exploring the route they took to these findings. In addition, Yixiao will share her experiences presenting their work at the Nebraska Conference for Undergraduate Women in Mathematics.

## March 2011

VIREOS: An Integrated, Bottom-Up, Educational Operating Systems Project with FPGA Support

Speaker: Dr. Marc Corliss

Thursday, March 3rd at 4:45pm

Room: Napier 201

(Refreshments will be served beforehand)

Abstract:

This talk will present the VIREOS project, a new operating system designed specifically for the classroom. VIREOS is a simple, Unix-like, operating system, which runs on the Larc educational architecture. A VIREOS/Larc system can either be simulated or run on a pre-configured FPGA. The VIREOS project is well integrated with an introductory computer architecture course (using Larc) and the assignments are structured in a similar fashion: using a bottom-up approach. The project includes several resources available on the Web, which help reduce the overhead of adopting VIREOS. Finally, VIREOS has been used in one operating systems course already, and, overall, it was well received by students.

A Basic Introduction to Knot Theory

Speaker: Adam Giambrone '08

Tuesday, March 8th at 4:45pm

Room: Napier 201

(Refreshments will be served beforehand)

Abstract:

The two main (unsolved) questions in the field of knot theory can be described as follows:The goal of this talk will be to introduce the field of knot theory to a general audience, beginning from the most basic foundations. After defining what a knot is, he will describe how to represent a knot by a two-dimensional diagram in the plane and also describe what it means for two knots to be "the same". Giambrone will then describe the idea of using knot invariants to tell knots apart and, if time permits, he will define the property of knot tricolorability and sketch the proof that this property is actually a specific type of knot invariant.

- Given a knotted loop of rope, is there a way to "untie it" to make the loop just a circle?
- Given two knots, is there a way to "deform" the first knot to turn it into the second knot?

Fractals: The rough and rugged curves they don't teach in calculus

Speaker: Dr. Jamison Wolf

Friday, March 25th at 4:15pm

Room: Gulick 206A

(Refreshments will be served beforehand)

Abstract:

The term "fractal" is often used to describe a set of points that can be obtained through some recursive procedure. Such a set of points could comprise a line or a surface, or could be a disconnected "dust." The recursive procedure repeats on every level of the construction, which tends to create patterns that are visible at every level of magnification. Fractals also tend to have some rather bizarre properties that are almost paradoxical. For example, the von Koch curve has an infinite length, yet the entire curve can be drawn inside a square of width one! This talk introduces some of the core concepts and applications of fractals by discussing several examples ranging from the classic Cantor set to the more general random fractals.

Model Theory and Definite Forms: An Elegant Solution to an Old Problem

Speaker: Dr. Laurel Miller-Sims

Tuesday, March 29th at 4:15pm

Room: Napier 101

(Refreshments will be served beforehand)

Abstract:

A rational functionF(x)=p(x)/q(x)is said to be positive definite ifF(x)>0for all real numbersx. These functions were of interest to mathematician David Hilbert who in his 1900 address to the International Congress of Mathematicians proposed 23 problems to shape the development of mathematics in the coming century. Hilbert's 17th Problem asked for a description of the set of all such positive definite rational functions. Although Hibert's 17th Problem was solved by Emil Artin in 1927, the techniques of model theory, a relatively new branch of mathematical logic, give an elegant solution to this old problem. I will give a basic introduction to model theory and a model theoretic proof of Artin's Nichtnegativstellensatz.

## April 2011

Eyeballs and ODEs

Speaker: Dr. Matthew Noonan

Friday, April 1st at 4:15pm

Room: Gulick 206A

(Refreshments will be served beforehand)

Abstract:

You have to get your Differential Equations homework done fast in order to make it to a movie on time. What tricks can you use for reasoning geometrically about differential equations? Once you complete your work, how can you efficiently parallel park your car at the movie theater? And when you finally take your seat, how does your brain fill in missing details from the movie screen when part of your view is rudely blocked by somebody's head?

And what on earth do these three things have to do with each other!?

This talk will require only elementary calculus and vectors. No special knowledge of differential equations will be assumed.

Using FPGAs to Create a Complete Computer System

Speaker: Marcela Melara '12

Thursday, April 7th at 4:15pm

Room: Napier 101

(refreshments will be served beforehand)

Abstract:

An FPGA is a programmable soft-processor that can be used to implement complex digital circuits such as a processor for a computer. Marcela will describe some work she has done implementing a basic yet complete computer system on an FPGA for an architecture called Larc. A major task of this project was to add support for essential hardware devices such as a monitor, a keyboard and a small hard drive. Furthermore, she added architectural support for running an operating system called VIREOS, which includes support for a file system and timesharing, among other features.

## Our Next Colloquium

Turing Instability in Discrete Replicator Systems

Speaker: Alex Bryce '09

Thursday, April 28th at 7:15pm

Room: Napier 101

(Refreshments will be served at 7:00pm)

Abstract:

When analyzing a discrete reaction-diffusion dynamical system, one primary area of interest is locating where in the parameter space Turing instabilities occur. It will be shown that Turing instabilities cannot occur in the react then diffuse equations if all diffusion coefficients are equal. The Replicator dynamic is a system of equations that is used in evolutionary game theory applications to study behavior types in animal populations. Conditions for a Turing instability in first order discrete replicator systems will be discussed and illustrated with computer simulations of the results. Alex will also be happy to answer questions about going to graduate school in mathematics.

## Past Colloquia Series

Fall 2010 Spring 2010 Fall 2009 Spring 2008 Fall 2008

If you have interest in giving a talk or know of someone who does,

please contact Erika King at eking@hws.edu or at (315) 781-3355