# Spring 2013 Talks

February 5: Corey Jones
Title: The Four Color Theorem
Abstract: The Four Color Theorem is easy to state: If you have a (nice enough) map of countries, and you want to color them so that no two adjacent countries are the same color, then you never need more than four colors to do it! This theorem was proved in the 70’s, but its proof is controversial among mathematicians due to its heavy use of a computer. We will discuss the history of this theorem, and then prove the Five Color Theorem, which states you never need more than five colors to color our map, which is much easier than four!

February 12: Michael Hull
Title: RSA – An Introduction to Public-Key Cryptography
Abstract: Ever wonder how you can safely send your credit card number over the internet? The answer is RSA, the first widely used public-keycryptographic communications system. Using only elementary techniques from number theory, RSA allows you to send secure communications over public channels without a pre-arranged code. In this talk, we discuss the difference between public-key and private-key cryptography, and cover some basic ideas from number theory. Then we will show how to use RSA to encode and decode messages, and explain why this process works and why it is so difficult to crack.internet? The answer is RSA, the first widely used public-key cryptographic communications system. Using only elementary techniques from number theory, RSA allows you to send secure communications over public channels without a pre-arranged code. In this talk, we discuss the difference between public-key and private-key cryptography, and cover some basic ideas from number theory. Then we will show how to use RSA to encode and decode messages, and explain why this process works and why it is so difficult to crack.

February 19: Min Gao
Title: Happy 100th? Math Modeling Predicts Human Longevity…
Abstract: The human species has a unique age structure with extended juvenile and senescent phases. What determines the age structure of humans and what could extend the human life span? Some researchers believe we should focus on curing disease and replacing damaged body parts via stem cell therapies. Others believe we must slow the aging process at the cellular and molecular levels. All proposed longevity strategies, however, remain unproven. The age structure of human population is shaped under common biological challenges, including environmental conditions, exposure to infectious diseases, distribution of resources to maintain the viability of the reproductively active populations, and replacement of reproductive populations by their offspring. In this talk, we will explore the age structure of human populations over evolutionary time.

February 26: Professor Webb
Title: Nosocomial Epidemics, R0, and the Hippocratic Oath
Abstract: nos-o-co-mi-al (adjective) – originating or occurring in a hospital
“get down R0, know your place, do not torment the human race”
primum non nocere – first, do no harm
Nosocomial epidemics are an increasing threat to society. The microbes that cause these epidemics are increasingly resistant to antibiotics. In the US they cause more than 100,000 deaths each year and that number is increasing. R0 (pronounced R-naught) is a quantity derived from mathematical models that predict the course of an epidemic. It is obtained from various parameters that determine the transmission dynamics of the infection. If R0 1, then the epidemic will worsen. The Hippocratic oath is the promise of physicians to not make the condition of a patient worse. It is the fundamental precept of medicine. I will tell you how all these are connected. I will also tell you how to avoid being infected by a nosocomial infection. Nosocomial infections occur in specific locations in the US, and only in these locations. You will never suffer a nosocomial infection if you do not go to one of these locations. I will tell you where these locations are.

March 12: 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.

March 19: Jeremy LeCrone
Title: Limitations of Visualization and Representation in Mathematics: The gap between theory and practice
Abstract: All mathematical computations and constructions are performed within an idealized “mathematical” universe. Objects are constructed in this universe by way of precise formulae and properties: e.g. the unit circle is defined to be all points (x,y) which satisfy the property x^2 + y^2 = 1. How can one accurately represent these objects in reality? We analyze, manipulate, and predict the behavior of these objects within the mathematical universe, but we must always take special care when we try to transplant these objects into our own “physical” universe. We will discuss general limitations in talking about mathematical objects and discuss interactions with computer representations. In a society dominated by computers, it is easy to forget that the objects displayed on our computer screens are only rough approximations of the theoretical “mathematical” objects they represent. We will discuss the limitations of these approximate representations, some of the methods employed to “draw” them, and how we approximate the manipulations we are able to perform in the idealized mathematical realm.

March 26: Michael Northington