A Graphical Approach to Dynamical Systems

Hunter Basselet, Adam Case
and Daniel Jackson

Monday, March 24, 2008

3:45 pm in Ricker Addition 202

Semisimple Lie Algebras

Peter Hardy

Wednesday, March 12, 2008

3:45 pm in Ricker Addition 202

Searching for Maximal Chaos

Hunter Basselet

Adam Case

Daniel Jackson

Monday, November 19, 2007

3:45 pm in Ricker Addition 205

Cavalieri’s Principle

Mike Molinsky

Wednesday, October 17, 2007

3:45 pm in Ricker Addition 205

The diagram above shows:

To find the answer to this pressing question, you will have to attend the talk.

The Steiner Tree Problem

Russell Rainville

Wednesday, September 26, 2007

3:45 pm in Ricker Addition 205

How did Delta Airlines save money on its telephone bill? For calls between corporate offices AT&T billed its corporate customers on the total length of the edges in the smallest tree that connected all of the company offices. By adding an office Delta’s phone bill was decreased by over a million dollars a year.

Steiner’s Problem: Given a set of points in the plane, what is the smallest graph (graph with least sum of edge lengths) whose vertex set includes the given set of points?

What is a Matroid?

Lori Koban

Tuesday, April 3, 2007

11:30 AM in CC 006

Vector spaces have minimal dependent sets of vectors. Graphs have circuits. But in the world of matroids, minimal dependent sets of vectors and circuits in graphs are the same. I’ll introduce matroids in general as well as my favorite matroids, which come from labeling the edges of graphs with group elements.

The Steiner Problem on the Cone

Jamie Burwood, Bowdoin College

Monday, February 5, 2007

5:30 PM in Education Center 106

This talk is based on a paper coauthored by Caroline Nielson of the University of Southern Utah. The paper investigates the n-point Steiner problem on the thin cone. The Steiner problem involves finding the minimal path between a set of points, adding additional vertices if necessary. This problem has been investigated extensively on the plane and solved on the sphere, but no one has previously explored this question on a surface with a sharp point.

In order to reduce the problem on the cone to the problem in the Euclidean plane, the cone will be “cut” in such a manner that it collapses to a circular wedge in the plane. For the 3-point problem, one cut is sufficient to determine the minimal Steiner tree; however, for n-points, many more cuts must be made in order to find the solution. The talk will present an algorithm for making these cuts and constructing the Steiner tree

Fractal Images of Cremona Maps

Dustin Gage

Nov. 29, 2006

3:00 PM in Roberts 105

This talk is based on work done during the summer of 2006 by Dustin Gage†, Dan Jackson, and Dan Savage. We will discuss the single variable dynamics of a parameterized set of maps and focus on how visual representations of mappings on C² can facilitate a better understanding of their hyperbolic components. We developed a Java applet to assist our research by producing fractal images of Cremona maps, as well as images of other quadratic rational maps of interest. I will describe the hyperbolic components – the Escape Type in particular – and discuss the utility of visualization for more research in the field. The aim is to understand the variation of the dynamics - in particular hyperbolic dynamics - of Cremona maps. We will discuss the progress made towards this goal.

† The continuation of the work on visualization of quadratic rational maps is supported by a Wilson Scholarship.

A Preview of Eulerpalooza

Mike Molinsky

Wednesday, November 8, 2006

3:00 pm in Ricker Addition 205

Next year will mark the 300th anniversary of the birth of Leonhard Euler. A wide variety of publications, conferences and other events are being planned in honor of this great mathematician. This talk will briefly address the importance of Euler’s work, present a few examples of his proofs, and also summarize some of the upcoming events of Euler’s tercentenary celebration.

Coordinate Functions of Plane Cremona Maps I

Dan Jackson

Wednesday, October 18, 2006

3:00 pm in Roberts 105

This is part 1 of a series of 3 talks based on work done during the summer of 2006 by Dustin Gage, Dan Jackson, and Dan Savage. In this talk we will introduce rational mappings of C² and their extensions to P². This is a large class of mappings whose global dynamics are still not well understood. We will focus on a special class of these mappings and a parameter space formed from their coordinate functions. The aim is to understand the variation of single variable dynamics - in particular hyperbolic dynamics - in this parameter space. We will discuss the progress made towards this goal.

San Gaku and Other Problems in Various Geometries

Amanda Taylor

Wednesday, October 4, 2006

3:00 pm in Roberts 105

Japanese San Gaku problems are Euclidean geometry theorems colorfully inscribed on tablets and hung on shrines in ancient Japan as a form of worship. In this presentation, we explore how some of these theorems and others are transformed when reformulated in spherical and hyperbolic geometry. The basics of both geometries will be explained.

Amanda did this work with another student, Christy Hediger from Muhlenberg College, at a Summer Research Experience for Undergraduates Program at Grand Valley State University. She will also talk about the Experience and the presentation of their work that they did at MathFest this past August.

"A Few Mathematical Models of Infectious Disease"

Christina Hayes

3:30 pm Friday, February 17, 2006

Ricker 217

    We will briefly discuss the pathology of influenza in general, as well as avian influenza in particular. I will then present some simple models used in mathematical epidemiology to study the spread of diseases such as influenza, smallpox, and typhoid fever. Assuming only basic understanding of what a derivative is, I will present a qualitative analysis of the SIR model. Using this approach, we will address the questions: What is the final size of the epidemic? What proportion of the population escapes the epidemic? For the SIR model in particular, we will use parameter values associated with the Hong Kong flu outbreak which occurred in New York City – in the late 1960’s.

"What Do Fractions, Completing the Square and Derivatives Have In Common?"

Lori Koban

3:30 pm Monday, February 13

Roberts 207

    The Dwarf who prepares these posters (Russell Rainville) has no additional insight into the talk than that provided by the title. You will need to come to find out!

"Vertices, Faces and Edges: An Intuitive Approach to Euler's Formula"

Nathan Carlson

3:45 pm Wednesday, February 8, 2006

Roberts 205

    If you divide the plane or the surface of a sphere into "faces", what can you notice about the number of vertices, faces and edges and how might you notice this?

"Detecting Errors in Codes"

Nicholas Koban

3:30 pm Monday, February 6, 2006

Roberts 207

    Codes are used to transmit information; ciphers are used to hide information. "Words" are encoded in an electric signal. The signal travels along wires, through the air, and maybe through space. At the receiving end the electric signal must get decoded into "words". As you may know from your cell phone, along the way there is noise and interference. How can the receiver recognize errors in the signal?

"Chaos Games"

Eva Curry

3:30 pm Friday, February 3, 2006

Computer Center 102

    A chaos game is a probabilistic algorithm for visualizing certain self-similar sets, including many fractals. This talk will present some background necessary for understanding what a chaos game does. You will also have the opportunity to explore chaos games, probability, and some fractals that can be generated by a chaos game.

Prime Numbers and Hairy Fractions

Steve Bies

3:30 pm Monday, January 30, 2006

Computer Center 006

     What does it mean that 21,649 × 513,239 = 11,111,111,111? What does this have to do with converting fractions to decimals? We will work out the decimal form of

- it's easy!

"Multi-Million Dollar Baby:

A Tale of Mystery, Misappropriation, Money and Mathematics"

Mike Molinsky

3:40 pm Monday, October 24, 2005

Computer Center 006

       This talk will cover the history of the Archimedes Palimpsest, which sold at Christie's auction house for two million dollars in 1998. The talk will also discuss new insights the document is giving us into the work of one of the greatest mathematicians of all times.

Finding All Integer Solutions To

Russell Rainville

3:40 pm Monday, October 17 2005

Computer Center 006

       This fall Dan Jackson joined the Mathematics Faculty and his mathematical interests are in "Birational Correspondences between Algebraic Varieties". To introduce these terms to students I decided to give a concrete example. I will use a birational correspondence between two hyper-surfaces to find all the integer solutions to the equations above. In particular we will find all integer solutions to:

"1-dimensional Cellular Automaton using Rule 30"

Dustin Gage

3:40 pm Monday, October 3, 2005

Computer Center 006

       This could be subtitled "What I did at Summer Camp". Dustin will talk about the work that he, Elizabeth Lamb, and Briana McGarry did at the Undergraduate Mathematical Research Experience program at Central Michigan University. They were investigating the use of an Automaton to produce pseudo-random sequences of "0"'s and "1"'s for use in encryption.

"A Sporadic Finite Simple Group"

Paul Gies

3:40 pm Monday

September 12 and September 19, 2005

Computer Center 006

       The classification of finite simple groups is one of the great monuments of twentieth-century mathematics. The finite simple groups lie mostly in a few infinite families---A_n, the projective unimodular groups---but exactly 26 of the groups on the list are not members of an infinite family. The smallest of these "sporadic" groups is the Mathieu group M₁₂, a simple group of 720 elements that act sharply 3-transitively on the projective line over the field with 9 elements. These talks will attempt to explain what that all means and how it is known.