Undergraduate Colloquium

Spring 2016
Wednesdays 12:55 - 1:45
LCB 225

Pizza and discussion after each talk
Receive credit for attending
Past Colloquia

January 13 No Talk
January 20 Andrejs Treibergs: Minimal Surfaces: Nonparametric Theory
Abstract: Minimal surfaces are mathematical models of soap films. Surfaces which have the least area among surfaces that span a given closed boundary curve in three space are called a minimal. We shall deduce the partial differential equation of minimal surfaces using the calculus of variations. We’ll consider various special examples, such as the catenoid, helicoid and Scherk’s surfaces. We’ll compare and contrast minimal surfaces to harmonic functions which satisfy a different but related PDE, Laplace’s Equation. The geometry is simplified in the so-called nonparametric case, which just means that the surface is given as the graph of a function.

Slides are available: www.math.utah.edu/~treiberg/MinimalSurfacesSlides.pdf
January 27 Nelson Beebe: Newcomb, Benford, Pareto, Heaps, and Zipf: Are arbitrary numbers random?
Abstract: An arbitrary collection of measured numbers from various sources ought, it seems, to be random, but the surprising answer is quite different. The implications of this discovery are astonishingly broad, from mathematical curiosity, to accounting, criminology, demographics, fraud, linguistics, nuclear decay, taxation, terrorism, Web searching, and even the rise of Fascism in the early Twentieth Century, and the recent Greek debt crisis. Come and learn something of this fascinating subject that can broaden your view of what mathematics is good for, and perhaps even turn your planned career in another direction.
February 3 Stewart Ethier: Optimal play at the video poker game Jacks or Better
Abstract: There are 134,459 distinct initial hands at the video poker game Jacks or Better. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. One way to derive a hand-rank table involves finding the exact optimal conditional expected return, given the initial hand. In the case of Jacks or Better (paying 800, 50, 25, 9, 6, 4, 3, 2, 1, 0), this is a random variable with 1,153 distinct values, of which 766 correspond to garbage hands for which it is optimal to draw five new cards.
February 10 Thomas Goller: Is humanity doomed?
Abstract: We will investigate a non-zero-sum game in which perfect rational play leads to disappointing results. Pessimists will be tempted to conclude that the selfish, rational human species won't last much longer, but we will see that there is room for optimism. Come ready to play and find out whether second graders are the true masters of game theory!
February 17 Donald Robertson: The porisms of Steiner and Poncelet
Abstract: Draw two circles, one inside the other. Starting anywhere between the two circles we can draw a chain of circles tangent to both. In some cases the chain will close up on itself. Steiner's remarkable porism states that whether the chain closes does not depend on where we start. We will prove this during the talk, and discuss another such result due to Poncelet if time permits.
February 24 Daniel Lee: Vulgar finance, divine mathematics: sports gambling, financial derivatives, and arbitrage
Abstract: There's no such thing as a free lunch...or is there? We'll explore situations in which we can make a riskless profit (i.e., an arbitrage opportunity) by analyzing sports betting. Time permitting, we will dip our toes in the world of financial markets and apply similar reasoning there. The only prerequisites are a strong understanding of high school algebra and maybe a little calculus.

Slides are available: Vulgar Finance, Divine Mathematics
March 2 Mary Harges, Mitchell Norton, and Kirsen Sullivan: Alumni Career Panel
Abstract: Come hear from three of our recent alumni about how they found their first job after college, how the skills they learned as part of their mathematics major help them in their positions, and what advice they have for current students. We'll be hearing from Mary Harges (Qualtrics), Mitchell Norton (Connexion Point), and Kirsen Sullivan (BioFire Diagnostics). Students will have the opportunity to ask questions as well.
March 9 Aaron Bertram: Fun with Pi
Abstract: As we approach a pi day of unusually many significant digits of silliness (3/14/16), it is time once again to muse on this transcendent number and its appearances in mathematics. As the fundamental irrational number needed to express the volumes of unit spheres, not to mention sums of even powers of reciprocal integers, such as 1 + 1/4 + 1/9 + ... = pi^2/6, this extraordinary number pops up in all sorts of unexpected mathematical corners. We'll take a tour of some of these pi encounters, and there may be pie as well.
March 16 No Talk - Spring Break
March 23 Dick Canary - Distinguished Lecture Series: Non-Euclidean sports and the geometry of surfaces (P,G)
Abstract: Hyperbolic geometry was discovered in the 19th century. It was the first example of a non-Euclidean geometry, i.e. a geometry which satisfies all of Euclid's axioms except for the parallel postulate. Hyperbolic geometry was later discovered to be a model for the geometries of surfaces with at least two holes and is the prototypical example of a negatively curved geometry.

In our talk, we will attempt to obtain a visceral understanding of hyperbolic geometry by exploring what it would be like to live in hyperbolic space. We will focus on what it would like to play various sports, for example, baseball, golf and beach ball, in hyperbolic space. If time permits, we will discuss the classification of surfaces and how surfaces with at least two holes can be given a hyperbolic geometry.
March 30 Radhika Gupta: Morphing graphs into matrices
Abstract: Given a finite graph can you tell if it is connected? Can you count the number of connected components? Can you connect a given pair of vertices by a path of 10 edges? How about a path of 100 edges? How many colors are sufficient to color the graph??? In this talk we will first train to morph a graph into a suitable matrix and then armed with this tool we will unravel some of these questions.
April 6 Peter Alfeld: What is a slide rule?
Abstract: There was a time when calculators did not exist. That did not stop us from building the Boeing 747, or going to the moon. In those days engineers, scientists, and students used slide rules on a routine and daily basis in place of calculators. I will show several slide rules, explain how they work, and describe what kind of mathematical expressions can be evaluated with a slide rule. (There are tens of thousands.) We'll also have a drawing. The lucky winner will get a slide rule to keep.
April 13 Matthew Cecil: The Marriage Problem
Abstract: How do you know when to stop dating and settle down? You might be surprised to learn that mathematics has an answer for you! I'll discuss this interpretation of a classic problem and tell you how to optimize your chances of making the best choice. The talk will use some simple probability and series computations.
April 20 Stewart Ethier: The Mathematics of Texas Hold'em
Abstract: Texas hold'em is the most widely played form of poker today. Each player receives two hole cards face down. Then three community cards are dealt face up (the flop), then a fourth one (the turn), and finally a fifth one (the river). There are four betting rounds, pre- flop, post-flop, post-turn, and post-river. A showdown follows, with the best five-card poker hand winning. As they say on television, "It takes a minute to learn and a lifetime to master."

We begin with some elementary considerations and then turn to the difficult question of how to rank the 169 distinct initial hands. We then use this information to illustrate how a particular hand might be played by a mathematically inclined player.