AlexDOPEAF

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

Spring 2018

Date

Presenter
Support
Institution
3/21/18

Su Ji Hong
Vince Longo
William Jewell College


Introduction to Cluster Algebras



An n x m matrix is said to be totally positive, if all of the n x n minors of the matrix are positive.  Then in the case of 2 x m matrix, there are m choose 2, or m(m-1)/2 minors to check before determining whether the matrix is totally positive.  As m gets larger this number grows fast.  However, we only really need to check 2m-3 minors to determine the total positivity of 2 x m matrix.  We'll extend the idea of the proof to find the generators of cluster algebras given by a quiver.  The cluster algebra was introduced by Fomin and Zelevinsky in 2002 and it has been studied widely since then.  The type A_n cluster algebras have been studied well; we can find the cluster variables of these cluster algebras in multiple ways including T-path and snake graph.







3/28/18

JD Nir
Paula Egging
University of Nebraska-Kearney


This Title is False: Hilbert, Godel, Turing and the Beautiful Futility of Mathematics




In a well known XKCD comic, scientific fields are arranged by purity with mathematics all the way at the end labeled "more pure."  We love math because it is rigorous and clear cute; there's a right answer and we know how to find it.  We deal with truth and certainty, right?

In this talk, we examine the foundation of these claims.  Does math rest on a solid bedrock of truth, or is it turtles all the way down?  What does it mean to be "true" anyway?  We will investigate the very heart of mathematics and find it is not the well-oiled machine we pretend it is.  After pulling back the curtain and seeing math for what it really is, will you still find it beautiful?







3/29/18

Lara Ismert
Erica Miller
Wayne State College


An Exploration of the Noncommutative World




Quantum mechanics is the best theory we have to describe micro-scale interactions in our universe.  Many consider the mathematical language of quantum mechanics to be "non-commutative algebra."  You might ask, "Why non-commutative?"  Well, you may have heard of the Heisenberg Uncertainty Principle, which asserts that we cannot simultaneously know where a quantum particle is and how fast it is going.  This mathematical principle is manifested in the strange phenomenon of measuring the position of a particle and then its momentum, and getting a totally different result than if the particle's momentum had first been measured and then its position.  In this talk, we will prove the Heisenberg Uncertainty Principle in a certain case using methods from calculus, and we will explore several more abstract geometric settings where commutativity fails, and non-commutativity prevails!







3/30/18
 
Vince Longo
Austin Eide
Missouri Western State University


Telling Physical Objects Apart Using Mathematics




Most people think of math as a way to use numbers or letters to represent or model real world situations.  However, in some branches of mathematics, the focus shifts to actually dealing with the physical objects themselves, such as a donut, a coffee mug, or a knotted up pair of headphone wires, and using math to attach a number, variable, or certain property to the object to be able to differentiate the objects from one another.  In this talk we will give a very light introduction to what this field of math (usually called topology) is all about without getting too bogged down by the numbers and details.  This talk will be geared towards undergraduates, and no prior math background will be assumed.







4/11/18

Alyssa Whittemore
Matt Reichenbach
NW Missouri State University


Prime Vertex Labelings of Some Families of Graphs




A simple n-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers 1, 2, 3, ... , n such that adjacent vertices have relatively prime labels.  There are many known families of graphs that have a prime vertex labeling (and some that don't).  I will present previously unknown prime vertex labelings for new families of graphs, some of which are special cases of Seuod and Youssef's 1999 conjecture that all unicycle graphs have a prime labeling.  No prior graph theory knowledge will be assumed.







4/13/18

Marla Williams
Erica Musgrave
Benedictine College


Knot Theory and Beyond




Knot theory has been of interest to mathematicians since the late 19th century, yet knot diagrams are simple enough to be understood by anyone - mathematician or otherwise - who sees them.  While this doesn't mean knot theory is simple or that knots are easy to work with, you might ask: what other areas of topology deal with complicated objects that can be represented by relatively simple diagrams?  This talk will touch on a few such areas, and naturally will involve a number of pictures.