# Great Plains Alliance

The Great Plains Alliance (GPA) was initiated in 2017 in order to connect UNL mathematics graduate students with speaking opportunities at nearby institutions.

Please email Thomas Kindred at thomas.kindred@unl.edu or Alex Zupan at zupan@unl.edu to volunteer as a speaker or a support role or to request a student talk at your college or university.

Current       Past       Members

Fall 2018

 Date Presenter Support Institution 10/3/18 Katie Tucker Sara Myers NW Missouri State University Local Moves on Knots Mathematical knots are smooth embeddings of a circle into 3-space.  Knots are sometimes examined by considering diagrams in the plane, which leads to the question:  How do properties of a knot change when we alter a region of the diagram?  In this talk we discuss some local moves on knots and their applications to knots in proteins. 10/9/18 Aurora Marks Dylan McKnight Wayne State College Think Like a PAC MAN Ghost The decision process that a PAC MAN Ghost makes can be modeled by a mathematical model of a computer called a finite state automaton (FSA).  We'll discuss another real-life example of an FSA and the details of this mathematical view of computation. 10/11/18 Stephanie Prahl Jackson Morris University of Nebraska-Kearney Bounded Operators and When Size Matters In a plane, there's a natural way to measure length: usually, straight-line distance.  This isn't the only way to measure length, though.  The distance from your house to the grocery store might instead be measured in driving distance, for example.  It turns out there are many ways to think about length in the plane.  We can also think about what length should mean in less intuitive spaces; for example, what should the "length" of a function be?  We will explore these different ways of thinking about length and use them to motivate the idea of bounded linear operators. 11/6/18 Matt Reichenbach Collin Victor Augustana University Structured Population Models in Mathematical Ecology Ecologists and wildlife managers want to know how they can keep biological populations healthy; that is, they don't want a population to die out or to explode.  However, they can't run experiments on wild populations because that usually costs too much money, or they risk irreparably damaging a population.  Thus, biologists use mathematical models and computers to study populations.  In this talk, I will introduce a number of "structured" population models.  These models make use of physiological differences, like the size of a fish or the developmental stage in grasshoppers.  Biologists use matrices, differential equations, and more recently integral operators, to stimulate structured populations in the wild.  I will give examples of each of these models, with lots of pictures.  The mathematical details should be accessible to anyone who has taken calculus. 11/14/18 Ariel Setniker Paula Egging Benedictine College Fractional Calculus: An Analog of Traditional Calculus as We Know It The derivative is at the heart of mathematics and specifically calculus, so why not extend this idea?  What does it mean to take a half derivative?  A "pi-th" derivative?  These are the questions that sparked the area of fractional calculus.  In this talk, we will investigate these intriguing questions and draw comparisons between traditional calculus and fractional calculus.  Time permitting, we will explore some of the various applications for which fractional calculus is well-suited. 11/16/18 Austin Eide Nicholas Meyer Drake University The Mathematics of Gerrymandering Gerrymandering, or the act of drawing political boundaries to favor a certain candidate or party in elections, has been a reality in the U.S. for most of its history.  In fact, the term "gerrymander" itself refers to a particularly amphibious-looking state senate district approved in 1812 by the then-Massachusetts governor Elbridge Gerry.  Since then, hundreds of congressional districts in the U.S. have gained infamy because of their peculiar shapes--examples include the late North Carolina 12th district and the still-active Illinois 4th.  However, not all gerrymanders contain offensively-shaped districts, and indeed some of the most effective gerrymanders appear geometrically sound.  How can we determine that a plan is a gerrymander in the absence of poorly-shaped districts?  In recent years, mathematicians have developed tools which are able to do just that.  I'll discuss some of these tools and the ways in which they're being applied to real cases of gerrymandering today.  Mathematical topics will include graphs, Markov chains, and some geometry, but no prior knowledge is needed. 11/30/18 David McMorris Nicole Buczkowski Creighton University Using Optimal Control Theory to Model Resource Allocation in Annual Plants The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season.  Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process.  In this talk we will discuss some introductory optimal control theory as well as two different models for resource allocation to roots, shoots, and fruits in annual plants.  In each model we will examine how optimal control theory can be applied to determine the optimal resource allocation strategy for the plant throughout its growing season.