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.
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(m1)/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 2m3 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
Tpath and snake graph. 

3/28/18 
JD Nir 
Paula Egging 
University of NebraskaKearney 

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 welloiled 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 microscale
interactions in our universe. Many consider the
mathematical language of quantum mechanics to be
"noncommutative algebra." You might ask, "Why noncommutative?"
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 noncommutativity 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 nvertex 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. 