February 4: Emily Marshall
Title: The Mathematics of Gerrymandering
Abstract: The American Heritage Dictionary defines gerrymandering as the act of “dividing a geographic area into voting districts so as to give unfair advantage to one party.” The problem of gerrymandering has led to the development of several mathematical measures of shape compactness, some of which have been used in court cases to argue for or against the legality of congressional redistricting plans. In this talk, we will show how the notion of convexity can be used to detect irregularly shaped districts. We will explore both theoretical and empirical aspects of this convexity-based measure of shape compactness.
February 11: Justin Fitzpatrick
Title: Mighty Morphin’ Power Series
Abstract: You might know that e^{i*pi} = -1, but do you know where this classic formula comes from? You might know that the infinite sum of 1/n^2 converges, but do you know what it converges to? In this talk we introduce power series not only to answer these questions but also several other questions that are much more easily solved using power series than by the standard techniques taught to first- and second-semester calculus students. February 18: Alexandr Kazda Title: Symmetries Abstract: Humans like symmetries. Ever wonder about the possible shapes that we can use to tile a floor in a symmetric manner? And how do we even describe what a “symmetry” is? For example, the circle, square and equilateral triangle are all highly symmetric objects, but they are somehow not symmetric in the same way. We will take a look at how to work with symmetries using group theory.
February 25: Marcelo Disconzi
Title: Some Ideas About Curvature
Abstract: The notion of curvature is of paramount importance in modern mathematics and physics. In this talk, I’ll introduce the concept at an elementary level, appealing to the intuition that comes from curves and surfaces in R3.
March 11: Cameron Browne
Title: Chaos and Population Dynamics
Abstract: Theoretical models and population data in ecology often show oscillatory and chaotic behavior. In this talk, I will introduce this subject by considering the logistic difference equation population model. We will see that by varying the growth parameter in this model, a transition from stable steady state to oscillations to chaos occurs, known as a period doubling bifurcation cascade. We will also discuss the problem of detecting chaos in ecological data.
March 18: Michael Northington
Title: Probability and March Madness
Abstract: In this talk, we will cover the basic rules of probability theory and look at a few simple but counter-intuitive results. Also, we will look at an interesting application of probability and statistics where a Markov chain is used to rank college basketball teams. As it turns out, this method, developed by researchers at Georgia Tech, has been successful when compared to other ranking systems (such as RPI, AP poll, ESPN poll, Sagarin rankings, etc.) in predicting the outcome of NCAA tournament games.
March 25: Charles Conley
Title: 1=2
Abstract: Much like a golf course, math has scenery that’s better to look at than it is to play in. Let’s have fun with a lighthearted look at some of these mathematical sand traps, waterfalls, and ice bergs. Once we know how they work,maybe we can steer around them.
April 1: Josh Sparks
Title: Mathematics Gone Wild! Mathematical Phenomena Found in Nature
Abstract: The world of math is a awfully neat place. Many facets of nature have instinctively borrowed the rules of mathematics that we have discovered through modeling, game theory, combinatorics, and a myriad of other disciplines. This talk will address some of the ways one can apply the rules of math to make sense of the vast universe around us, all in the epic period of an hour. Enjoy!