Title: R as a vector space over Q, with an interesting consequence
Speaker: Dustin Hedmark

Abstract: We will look at the real numbers as a vector space over the rational numbers. After reviewing relevant linear algebra terminology, we will show that this is an infinite dimensional vector space. Next, we will use the vector space R over Q to show that there does not exist a tiling of a rectangle of dimensions 1 by x with squares, where x is an irrational number.

David Murrugarra will talking about some research he did over the past year with two UKY undergraduate students. The title and abstract of his talk are below. Please come and ahangout with other mathematically minded students. There will be pizza.

Title: Estimating Propensity Parameters using Google PageRank and Genetic Algorithms

Abstract: Stochastic Boolean networks, or more generally stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. The standard updating schedules include the synchronous update, where all the nodes are updated at the same time and gives a deterministic dynamic, and the asynchronous update, where a random node is updated at each time step that gives a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. SDDS is a modeling framework that considers two propensity values for updating each node, one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and the other when the update is negative, that is, when the update causes it to decrease its value. This extension adds a complexity in parameter estimation of the propensity parameters. This talk presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution and then with the use of a genetic algorithm the propensity parameters are estimated.

Title:  My favorite unsolved math problems, interesting new developments in psychology, and various reasons why infinity makes me nervous

Abstract:  Mathematicians and scientists spend much of their time thinking about how to solve problems that no one knows how to solve. There are lots of cool unsolved math problems that are easy to explain and think about (even for elementary and high school students), but that are nevertheless incredibly hard for professional mathematicians to make any progress on. In this talk, I'll share a few of my favorite unsolved math problems, and discuss why they are my favorites. Along the way, we'll talk about some recent research in psychology and sociology that comes into play when people struggle to understand the mathematical unknown.

Title:  Generatingfuncitonology (Or looking for a closed formula for the Fibonacci sequence)

Abstract:  A beautiful formula for the integer sequence of Fibonnacci numbers, already known by Abraham de Moivre in the 17th century, will give us enough motivation to introduce a very useful technique in Combinatorics to find closed formulas for sequences defined by a recurrence relation.

When can integers be written as the sum of squares?

From Pythagoras, to Fermat, to Legendre, mathematicians have been interested in representation of integers by sums of squares. Legendre's beautiful 4 square theorem states that any positive integer can be represented as the sum of 4 squares. For example 1+4+4+9=18. One easily checks that 7 cannot be written as the sum of 3 squares. How well can we do with two squares?

Title:  The Actuarial Profession

Sponsored by:  Mathematical Economics