# Fall 2015 Talks

September 29: Michael Northington V
Title: Math and Music
Abstract: Software tools such as Garage Band and Audacity, allow musicians to analyze and create music, but how do these tools work? In this talk, I will introduce a branch of mathematics called harmonic analysis and its most important tool, the Fourier Transform. I’ll show how this can be used to break down a short piece of music into its frequency components, and (hopefully) show how some data analysis techniques can be used to allow a computer to identify what chords/notes are being played based on these frequencies.

October 6: José Gil-férez
Title: The Hero and the Hydra: A Journey to the Infinity and Beyond (and Back Again)
Abstract: The Hydra, with its many, many heads, poisonous breath, and blood so venomous that even its scent is lethal, is guarding the entrance to the Underworld. The hero needs to slain the monster, but with each head that is severed, the rage of the beast grows and many more heads spring up.
We consider our duty to help the hero and realize that, for the task to be accomplished, all that is needed is to know the number of the beast. But its number is not part of this finite world of ours, and the search is going to lead us up the ordinal stairs, to the infinity and beyond. With good fortune on our side, we shall return, descending from the hinterlands of infinity in only a finite number of steps, just on time to defeat our foe.
From this journey, we will learn about our limitations as finite beings, and how the multiple powers of our imagination would prove necessary to overcome them.

October 13: Glenn Webb
Title: A Model of the Ebola Epidemics in West Africa Incorporating Age of Infection
Abstract: A model of an 2014-2015 Ebola epidemic in West Africa is developed with infected individuals structured according to disease age (time since acquiring the infection). The transmission of the infection is tracked by disease age through an initial incubation phase, followed by an infectious phase with variable transmission infectiousness. The removal of infected individuals is dependent on disease age, with three types of removal rates: (1) removal due to hospitalization (isolation), (2) removal due to mortality separate from hospitalization, and (3) removal due to recovery separate from hospitalization. Model simulations for Liberia, Sierra Leone, and Guinea indicate that successive stages of increased and earlier hospitalization of cases have resulted in mitigation of the epidemics.

October 27: Oleksandr Vlasiuk
Title: Pocketable Mathematical Problems
Abstract: It is well-known in the mathematical community that one does not in fact need computers, blackboards or even pen and paper to work on a math problem. Mathematicians enjoy the ability to conduct research in very hostile environments — sometimes even while sunbathing on a beach!
Naturally, inspirations for some mathematical questions come from everyday experiences: commuting to work, riding a Mars rover, folding paper or walking in the woods. Occasionally a back-of-the-envelope calculation leads to deep ideas in quite unexpected areas of mathematics.
We will deal with the natural and simple problems here, leaving connections to the state of the art science as an easy exercise for the listeners.

November 3: Zach Gaslowitz
Title: The Trouble with Voting
Abstract: We will explore some of the surprising mathematical challenges one runs into when trying to turn a pile of ballots into a single winner. How do we decide who should win, and how does this question influence our democracy as a whole?

November 10: Johanna Stromberg
Title: A dress with ambiguous colours
Abstract: Do you remember the dress that exploded the internet because no one could agree if it was black and blue or white and gold? Did you ever wonder why that could be? In this talk we explore the mathematics behind how colours are rendered on a computer screen, and try to answer why black and blue can end up looking like white and gold.

November 17: Ryan Solava
Title: How Many Crayons? (Graph) Coloring Problems
Abstract: A question that you might (or might not) ask is how many different colors of crayons do you need so that for any page of a coloring book, you can color each region, so that no two adjacent regions have the same color. This question is more commonly phrased in terms of maps, and the answer is given by an important theorem, which I won’t name here because the name gives away the answer. In this talk, we will explore this problem and the more general topic of graph coloring. Together we will get a glimpse of discrete mathematics and combinatorics, a side of math that you don’t often get to see in required math courses.

December 1: Colin Klaus
Title: Multiscale Modeling in Modern Day Biology
Keywords: Homogenization, Concentrating Capacity, G-Protein, Vision
Abstract: The impact of mathematical modeling upon sciences such as physics and astronomy has proved a crowning intellectual triumph. Thanks to a small handful of penetrating ideas, a vast range of otherwise inscrutable physical observations were miraculously understood and conceptually organized. (If you don’t believe me, google “Rudolphine Tables!”) This is not a removed moment in history. Today, now, experimental biology stands in that same position, needing breakthrough ideas that can render new understanding and organize their enormously amassed data sets. In the context of a specific G-protein signaling cascade underlying Visual Transduction (eyesight!), we’ll explore what contributions mathematical modeling can bring to biology. More generally, we’ll touch on what circumstances make a situation ripe for potential modeling discoveries.