Graduate Student Presentations

Presentations

Graduate Student

Spring Semester 2024

Math Graduate Student Presentations

Spring Semester 2024

DateSpeakerTitle/Abstract

M.S. Talk

April 26, 2024

12:15-1:15pm

ENG 247

Jonathan ThompsonTITLE: “Supervised and Unsupervised Learning via the Kernel Trick”

M.S. Talk

May 2, 2024

12:30pm

OSB B138

Joseph Noernberg

TITLE: Adaptive Spectral Numerical Method for Solving PDEs via Conformal Maps

ABSTRACT: PDEs can be spontaneous and difficult to solve, especially when they involve poles or branch cuts. In this talk, we introduce an adaptive spectral numerical method that is intended to solve such PDEs. We also analyze the use of conformal maps and their effect on reducing error around error-prevalent regions. Abstract

M.S. Talk

May 2nd, 2024

1:00pm

OSB B138

River VanIwaarden

 
Fall Semester 2023

Math Graduate Student Presentations

Fall Semester 2023

DateSpeakerTitle/Abstract

M.S. Talk

November 30, 2023

12:30pm

OSB B215

Jack Nagle

TITLE: "Evolutionary Algorithms and their Applications"

Abstract

Spring Semester 2023

Math Graduate Student Presentations

Spring Semester 2023

DateSpeakerTitle/Abstract

M.S. Talk

April 27, 2023

12:30-1:00pm

OSB B136

Stephanie Klumpe

TITLE: “Equivalent Codes From Finite Fields”

ABSTRACT: Equivalency of codes, in regards to, encryption becomes a different question when we remove ourselves from the typical alphabet. Historically, people would take messages and use maps on the alphabet to translate the messages into equivalent statements that look different on the surface. In the context of fields, this is where MacWilliams did her work and showed that, under certain circumstances, we can still show certain codes are equivalent even if they look different. We will explore her work and show with examples how this can be done, and then look to what lies beyond MacWilliams' initial work.

M.S. TalkTroy Johnson 
Fall Semester 2022

Math Graduate Student Presentations

Fall Semester 2022

DateSpeakerTitle/Abstract

M.S. Talk

Nov. 29, 2022

12:30-1:00pm

OSB B136

Jack Kessler   TITLE: Numerical Simulation of Lightning

M.S. Talk

Nov. 29, 2022

1:00-1:30pm

OSB B136

Carl Cassidy    TITLE: The Axiom of Choice and its Equivalences

M.S. Talk

Dec. 1, 2022

12:30-1:00pm

OSB B134

Kaden Ripingill

TITLE: Numerical Approximation of a Helmholtz Equation on a Generalized Domain Using a Meshfree Method

ABSTRACT:

The Helmholtz equation is the eigenvalue problem associated with the Laplace operator.  We often encounter this equation in the study of natural phenomenon such as wave propagation.  To numerically approximate the eigenvalues of a Helmholtz equation we may use a meshfree method.  An advantage of meshfree methods is that we may define our problem on a domain with complex geometry.  In particular, we can apply a meshless method to approximate the solution of a Helmholtz equation on a two-dimensional generalized domain.

M.S. Talk

Dec. 1, 2022

1:00-1:30pm

OSB B134

Jarrid Carroll-Frey

TITLE: Neural Networks and Universal Approximation: A Fundamental Result

ABSTRACT:

Artificial neural networks have been gaining in popularity over the past few decades due to their ability to solve problems arising in various areas of applied mathematics and engineering. More recently a new application in particular interest of the scientific computing community has materialized, and that is the ability for neural networks to solve partial differential equations. In general, finite element methods (FEMs) are used to solve PDEs in practice, but these methods have some limitations due to the required mesh size. Neural networks offer a promising alternative to FEMs due to their ability to bypass some of these limitations. However, the ability of neural networks to solve partial differential equations hinges upon the fundamental result that neural networks are universal approximators. That is, given any arbitrary function, there exists a neural network that approximates this function to any desired degree of accuracy. In this talk, we will rigorously prove this result.

M.S. Talk

Dec. 1, 2022

4:45-5:15pm

OSB B134

Kristen Gearhart

TITLE: An Introduction to Homology

ABSTRACT:

In this talk, I will motivate the study of homology and introduce different homology theories. Along the way, I will provide examples to illustrate concepts and demonstrate basic calculations. I will conclude the talk by mentioning a few big theorems that can be proven using homology, and I will discuss both categories and functors arising from this study and a path in the opposite direction.

Spring Semester 2022

Math Graduate Student Presentations

Spring Semester 2022

DateSpeakerTitle / Abstract

PhD Dissertation Defense

April 15, 2022 4:30pm-6pm

OSB 213

Michael Zowada

TITLE: Classification and Analysis of Rational Lump Solutions to the Kadomtsev-Petviashvili I Equation

ABSTRACT:

The Kadomtsev-Petviashvili (KP) I equation is a 2+1-dimensional nonlinear partial differential equation which describes propagation of small-amplitude quasi-two-dimensional dispersive waves. They are known to model ion-acoustic waves in plasmas and shallow water waves. 
Mathematically, the KP equation belongs to the special class of completely integrable equations which admit large classes of exact solutions. In this thesis a large family of nonsingular rational solutions of the KPI equation are investigated. These solutions referred to as lumps, are multi-peaked waveforms localized and decaying in the xy-plane, and are interesting because of their anomalous scattering after collision. A detailed study of the dynamics of these lumps, their interaction properties and long time behavior is carried out analytically, and their stability is investigated numerically. Furthermore, the thesis provides a complete classification of this class of rational solutions by establishing a deep connection between the solution class and the representation theory of symmetric groups and partitions of integers. This relationship is further exploited to explain the richness of the surface wave patterns formed by these solutions, and which are shown to be related to the zero distributions in the complex plane of certain well known polynomials arising in the theory of Painlevé equations. 

Fall Semester 2019

Math Graduate Student Presentations

Fall Semester 2019

DateSpeakerTitle / Abstract
M.S. Talk

December 4, 2019 4:30pm
ENG 239		Veronica Marth

TITLE: Classification of Divisible Abelian Groups

ABSTRACT: 

We know that abelian groups are Z-modules. A divisible abelian group is closed under “division” by positive integers. We will consider both the torsion and torsion-free divisible abelian groups as we explore the Classification of Divisible Abelian Groups Theorem and outline its proof. We will conclude by examining some of the consequences of the classification theorem. 

 

Spring Semester 2019

Math Graduate Student Presentations

Spring Semester 2019

DateSpeakerTitle / Abstract
PhD Dissertation Defense

April 12, 2019 1:30pm
OSB A204		Alyssa OrtizTITLE: Inverse Scattering Transform and Solitons for Matrix Nonlinear Schrödinger Systems and for The Deficusing Ablowitz-Ladik Equation  

ABSTRACT: N/A

PhD Committee: Dr. Barbara Prinari (Chair), Dr. Radu Cascaval, Dr. Greg Morrow, Dr.Oksana Bihun, Dr. Marek Grabowski (Physics)
M.S. Talk

May 2, 2019 12:15pm-12:30pm
 		Clark MourningTITLE:  Generalized Pseudispectral Method and Zeros of Orthogonal Polynomials 

ABSTRACT: PDF
M.S. Talk

May 2, 2019
12:30pm-1:00pm		Rachel DrawbondTITLE: Every Principal Ideal Domain is a Unique Factorization Domain

ABSTRACT: N/A
M.S. Talk

May 2, 2019
1:00pm-1:30pm		Katerina GkogkouTITLE: Interaction of 2 Solitons in The Square Matrix Nonlinear Schrödinger Equation 

ABSTRACT: PDF
Summer 2018

Math Graduate Student Presentations

Summer Semester 2018

DateSpeakerTitle / Abstract
July 18, 2018 4:30pm
ENG 239		Jacob KarnTITLE:  Rings whose prime spectrum has certain arithmetical closure properties

ABSTRACT: PDF
Spring Semester 2018

Math Graduate Student Presentations

Spring Semester 2018

DateSpeakerTitle / Abstract
April 30, 2018 12:15pm
ENG 239		Allison DonahueTITLE:  Topology of Cantor Sets 

ABSTRACT: PDF
April 13, 2018Meng LiTITLE:  A Simulation on Campus Pedestrian Traffic 

ABSTRACT: With the ever-growing population of university campuses, the understanding of pedestrian flow throughout them becomes more and more important as time goes on. In this project aim to model the paths that people on a university campus will take to get from one place to another. The project simulates the UCCS campus pedestrian traffic based on the data from Fall 2014. The project also addresses the path choosing processes considering the capacities of each available paths on UCCS main campus. The model considers the idle students locations with stochastic approach.
April 13, 2018Justin GarrishTITLE:  Radial basis function-generated finite differences (RBF-FDs): supplementation with polynomials and application to a steady-state flow problem 

ABSTRACT: RBF-FD methods have been gaining popularity to approximate solutions of partial differential equations due to their combination of simplicity, accuracy, and flexibility, especially in irregular geometries. That being said, direct substitution of RBFs for traditional basis functions (e.g. cubic splines) is not enough to guarantee accurate or stable computational solutions. Supplementation of RBF-FD with polynomials will be presented as an approach to overcome these shortcomings, and the impact of polynomial degree on its efficacy will be illustrated on a benchmark problem. A modern approach to domain discretization permitted by this method will be demonstrated. In particular, we apply RBF-FD with supplementary polynomials to the compressible Euler equations in order to simulate two-dimensional steady-state flow around an object enclosed in a tube.
Spring Semester 2017

Math Graduate Student Presentations

Spring Semester 2017

DateSpeakerTitle / Abstract
April 7, 2016 12:00-1:30pm
OSB A215		Tommy McDowellTITLE:  Numerical Study of the Stem in 3142-Soliton Solution of KP 

ABSTRACT: PDF
Spring Semester 2016

Math Graduate Student Presentations

Spring Semester 2016

DateSpeakerTitle / Abstract
April 7, 2016 12:00pm OSB A327Ikko SaitoTITLE: Traceless Matrices that are not Commutators which each equivalence class contains a unique possessing these ABSTRACT: By a classical result, for any field F and a positive integer n, a matrix Mn(F) is a comumutator if and only if it has trace zero. This is no longer true if F is replaced with an arbitrary ring R. But the only known example of matrices which have trace zero and are not commutators are of the size 2x2. The purpose of this thesis is to construct an nxn matrix for any positive integer n>2 which has trace zero but is not a commutator.
April 7, 2016 1:00pm OSB A327Katherine CliffTITLE: An Introduction to Information Geometry equivalence mentation class contains a unique possessing these ABSTRACT: Information Geometry is the application of differential geometry to probability theory. After introducing the basic notation and vocabulary of information geometry, we will examine some fundamental results relations to the asymptotic theory of information and the relationships between statistical manifolds
Fall Semester 2015

Math Graduate Student Presentations

Spring Semester 2015

DateSpeakerTitle / Abstract
September 22, 2015 12:30pm-1:00pm ENG 239Reece AdragnaTITLE: An Introduction to Information Geometry equivalence mentation class contains a unique possessing these ABSTRACT: Information Geometry is the application of differential geometry to probability theory. After introducing the basic notation and vocabulary of information geometry, we will examine some fundamental results relations to the asymptotic theory of information and the relationships between statistical manifolds
Summer Semester 2015

Math Graduate Student Presentations

Spring Semester 2016

DateSpeakerTitle / Abstract
July 16, 2015Luke HarmonTITLE: A set-theoretic foundation of mathematical induction ABSTRACT: We will use Godel-Bernays set theory, with the 'standard' axiom of infinity replaced by Tarski's infinity axiom, to rigorously construct the set of natural numbers. This construction will then be used to justify the ubiquitous Induction Principle.
August 6, 2015Kathryn ArthurTITLE: Markov Chains
Fall Semester 2013

Math Graduate Student Presentations

Fall Semester 2013

DateSpeakerTitle / Abstract
December 17, 2013Henri NdayaCoding Theory - Error correcting codes: A special look at the Reed-Muller Codes ABSTRACT:The purpose of my presentation is to focus on linear codes and conclude with a special look at a family of codes (the Reed-Muller Codes) defined recursively with interesting properties and easy code decoding algorithms.
Spring Semester 2013

Math Graduate Student Presentations

Spring Semester 2013

DateSpeakerTitle / Abstract
April 25, 2013Robert MarionMethod of Multiple Scales with an Application to Water Waves
April 25, 2013Katie HendricksAlgebraic Topology: Fundamental Groups
April 25, 2013Andrea EsslerLinear Programming The Simplex Method
April 25, 2013Gaetan DelavignetteModeling the Risk of Cancer
April 25, 2013Kevin EwingThe Richardson Arms Race Model-An Elementary Analysis and a Nonlinear Modification
April 25, 2013Ben SchoonmakerAn Examination of the K0 Groups of the Leavitt Path Algebras of some Cayley Graphs
Fall Semester 2012

Math Graduate Student Presentations

Fall Semester 2012

DateSpeakerTitle / Abstract
Dec 6, 2012David EnglandPsudospectral Methods for Optimal Control
Dec 6, 2012Joshua CarnahanNelder-Mead Method and Applications
Spring Semester 2012

Math Graduate Student Presentations

Spring Semester 2012

DateSpeakerTitle / Abstract
April 18, 2012James ParmenterGraphs of Leavitt Path Algebras: e A natural equivalence relation on finite acyclic directed graphs arises from the graded isomorphisms between finite dimensional Leavitt path algebras. We will identify graph-theoretic properties for which each equivalence class contains a unique possessing these properties.
May 1, 2012Tracey MorelandGravitational Effects on Blood Flow Velocity: How fast does blood flow through the arteries with each heart beat? In this presentation I will look at Womersley flow, a classical approach to calculating blood flow velocity. This approach assumes flow through a rigid tube, and uses concepts from fluid mechanics to model the flow velocity. Bessel functions and the Navier-Stokes equations are used in the model, and Fourier series are used to model the pressure gradient function. I will also examine an extension to the model to include gravitational effects on blood flow. Results will be given for various gravitational fields and for different animals.
May 1, 2012Jim EberleAbstract: When data is transmitted via satellite, or when you use a CD, errors can occur in the process of getting the data to you. When it is important that the data is correct, an error correction code must be embedded in the data. One of the popular means of encoding and decoding is "Convolutional Error Correcting Codes". These codes will be discussed in how data can be encoded and decoded, and how these codes are used.
Spring Semester 2011

Math Graduate Student Presentations

Spring Semester 2011

DateSpeakerTitle / Abstract
April 28, 2011Markus TyboroskiAn overview of the finite element method
April 28, 2011Richard NeelyThe Statistics Behind Cancer
Spring Semester 2010

Math Graduate Student Presentations

Spring Semester 2010

DateSpeakerTitle / Abstract
May 5, 2010Jennifer HolmesBrownian Motion and the Counterintuitive Aspects of Arcsine Law
May 5, 2010McKenna RobertsEvaluation of parameter effects in estimating non-linear uncertainty propagation
Fall Semester 2009

Math Graduate Student Presentations

Fall Semester 2009

DateSpeakerTitle / Abstract
Nov 13, 2009Steve HartmanProperties of the Hyperbolic Area Function
Spring Semester 2009

Math Graduate Student Presentations

Spring Semester 2009

DateSpeakerTitle / Abstract
April 23, 2009Matt GerholdtModeling the Chaotic Waterwheel
April 23, 2009Merida BassImaginary Numbers: A History
April 23, 2009Joseph MontgomeryMoving Frames In Differential Geometry
May 5, 2009Robyn MacivorUsing Fractals to Study the Structure of Trees
May 5, 2009Jason OcvirkStochastic Processes with Sports Standings
June 16, 2009Jeremy RiehlElliptical Geometry: A Closer Look
Spring Semester 2008

Math Graduate Student Presentations

Spring Semester 2008

DateSpeakerTitle / Abstract
April 24, 2008Brian WhiteAn introduction to the field of game theory, focusing on two person, zero-sum games with a short proof of von Neumann's Minimax Theorem
April 24, 2008Mihalo PopovicTopology of Pointwise Convergence of Sequences of Real Functions. (An example of non-metrizable topology)
April 24, 2008Jeff MarshThe Kuramoto Model
May 2, 2008Dustin KeckThe “Art” of Algebraic Groups and Tessellations
Summer Semester 2007

Math Graduate Student Presentations

Summer Semester 2007

DateSpeakerTitle / Abstract
July 2, 2007Dustin SchmidtEffects of Selection on Information Entropy in a Weasel Program
Spring Semester 2007

Math Graduate Student Presentations

Spring Semester 2007

DateSpeakerTitle / Abstract
April 24, 2007Travis SperoMacroscopic Traffic Modeling
April 19th, 2007Eric SullivanMathematics on the Rocks
May 1, 2007Shane PassonMethods of Control