# 2012-2013 Seminar Series

## Northern Spotted Owl

### Wednesday April 10, 2013

The endangered Northern Spotted Owl has sparked conflict between ecologists and the logging industry. The mathematics used to support conservation of the owl’s habitat initiates exciting applications of mathematical modeling and linear algebra.

## Congruent Numbers and Elliptic Curves

### Friday April 12, 2013

Can you determine a triangle with rational sides that produces an area that is an integer? Well if you can do it for any integer, you are well on your way to getting \$1,000,000. We will discuss how points of infinite order on specific elliptic curves can give us these triangles.

## Game of Life

### Wednesday April 17, 2013

The game of life models a population on a checkerboard under certain rules. Steady states occur when these “rules” force a pattern to remain unchanged. Using integer programming it is possible to find many interesting still life patterns on different size boards.

## Understanding the Levi-Civita Field

### Friday April 19, 2013

Did limits in calculus make you angry? There is a different calculus that does not discuss limits; instead it discusses infinitely small numbers, or the infinitesimals. By understanding the infinitesimals and the Levi-Civita field, we can apply them to eliminate limits from calculus.

### Monday April 22, 2013

When you take a knotted up piece of string and connect the ends together you get a mathematical knot. There are many different types of knots and polynomials can determine the equivalency of the knots. Come see how!

## Fractal Regularity

### Monday April 29, 2013

What do snowflakes, oil spills, and tree branches have in common? They are fractals—those pretty pictures where the more you zoom in the more it look the same. There is obviously some regularity, but what is it? Using graphical models we can investigate this regularity.

## Coloring M-Pires

### Friday November 16, 2012

Did you know any map can be colored using four colors? It has been proven that any map can be colored with four colors such that adjacent countries receive different colors. I will explore a variation of this problem using Empires. Empires are regions that do not have to be connected geographically. Every region in an empire must receive the same color. In addition, the empires next to it must receive different colors. I will prove the minimum number of colors needed to color such maps.

## Mathematical Knot Invariants

### Friday November 30, 2012

Mathematical knots are not the standard knots one may have made in boy scouts or girl scouts.  Mathematical knots  are a string whose ends are tied together to form a closed loop in three-dimensional space. In order to distinguish whether mathematical knots are different from one another, mathematicians look at knot invariants. Tricolorability and Fox r-colorings are two different knot invariants that will allow us to differentiate one type of knot from another type of knot.

## Bouncing Billiards

### Wednesday December 5, 2012

This is a study of trajectories of a bouncing billiard ball on a pool table with lengths that are relatively prime. Under certain conditions the ball will bounce indefinitely until it finds a pocket. How many times will the ball bounce? Which pocket will it land in? What happens if we change specific conditions?

## Modeling the Evolution of Life Cycles in Sexually Reproducing Organisms

### Monday December 10, 2012

One of the most fundamental aspects of any given organism is its life cycle, so we need to understand why the variation that is seen among life cycles came about. Come explore mathematical and computational models of this important problem in evolutionary biology.