Each semester the Department of Mathematics offers colloquium talks on a variety of mathematical topics. The department also hosts the Advanced Research Initiative series, featuring a distinguished guest speaker giving two talks.

## 2018 Spring Math Colloquia

**February 21**

Michael Otunuga (Marshall University)

Global stability for a (2n+1)-dimensional HIV/AIDS epidemic model with treatments

Smith Hall 518, 4:00pm

*Abstract:* In this work, we derive and analyze a (2n+1)-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treatment strategy of regular HIV testing and immediate treatment with Antiretroviral Therapy (ART) is investigated in the presence and absence of noise. By defining R(0,n), R(t,n) and **R**(t,n) as the deterministic basic reproduction number in the absence of ART treatments, deterministic basic reproduction number in the presence of ART treatments and stochastic reproduction number in the presence of ART treatment, respectively, we discuss the stability of the infection-free and endemic equilibrium in the presence and absence of treatments by first deriving the closed form expression for R(0,n), R(t,n) and **R**(t,n). We show that there is enough treatment to avoid persistence of infection in the endemic equilibrium state if R(t,n)=1. We further show by studying the effect of noise in the transmission rate of the disease that transient epidemic invasion can still occur even if R(t,n)<1. This happens due to the presence of noise (with high intensity) in the transmission rate, causing **R**(t,n)>1. A threshold criterion for epidemic invasion in the presence and absence of noise is derived. Numerical simulation is presented for validation.

**April 19**

Carl Mummert (Marshall University)

The number TREE(3), and counting down in base infinity

Smith Hall 518, 4:00pm

*Abstract:* The motivation of this talk is a peculiar situation from computer science. In some cases, we know that a program will eventually stop, but we have no way to concretely describe or even bound the number of steps the program will take. For one such program, the number of steps is a number TREE(3) so large that there is no concrete way to describe it or bound it from above.

This talk will introduce TREE(3) and the related result known as Kruskal’s theorem. We will look at some simpler versions of the theorem, leading us to a “base infinity” number system. This system is like base ten, but each digit can be arbitrarily large. We will see that counting down to 1 from a base infinity number is not as easy as it sounds.

The work on base infinity numbers is joint research with mathematics major Samantha Colbert.

## 2017 Fall Math Colloquia

**September 20**

Matt Davis (Muskingum University)

Non-transitive dice: Constructions, Complications, and Questions

Smith Hall 509, 4:00pm

*Abstract:* Non-transitive dice have been a source of fascination for mathematicians for over 50 years. We are given a set of dice which are numbered in strange ways. Each player chooses a die, rolls it, and the higher roll wins. Our intuition suggests that in any set of dice, one is the “best”. However, it turns out that it is relatively easy to construct a set of dice which are non-transitive – where most dice are strong against some opponents and weak against others. In this talk we will look at lots of examples of these fascinating objects, aiming for a goal of a single construction that allows us to create a set of dice in any desired configuration. We will also talk briefly about the much harder problem of finding the most efficient way to create such a set of dice.

**October 18**

Skye Smith (Service Pump & Supply, Huntington WV)

Three Things I Wish I Had Known When I Was a Math Major

Smith Hall 509, 4:00pm

*Abstract:* Since graduating from Marshall University with an applied mathematics degree in 2014, I have used my degree in several various business roles. Each position has provided a new way to use my mathematics degree in a business setting and each role brought new lessons I wished I had considered throughout my time as an undergraduate student. In this presentation, I will discuss the three things I wish I had known while I was a mathematics major at Marshall University. Addressing these three observations will help guide mathematics students who are hoping to use their skill set in a business setting at a time when math minds are more important than ever to companies undergoing digital transformations and embracing the era of big data.

**November 15**

Avishek Mallick (Marshall University)

Statistical Modeling of Discrete/Count Data

*Abstract:* In this talk, I will introduce the idea of Statistical modeling, especially in context of count data. We will look at different facets of data fitting like estimation techniques and criterion for assessing goodness-of-fit. A substantial part of the talk will be about modeling inflated count data. We will be looking at lots of real world examples. This talk is intended for a general audience and thus should be appropriate for Mathematics undergraduate and graduate students.

## 2017 Spring Math Colloquia

January 16

Carl Mummert (Marshall University)

Mathematical Induction: Through Infinity and Beyond

February 16

John Asplund (Dalton State University)

Vertex Colouring Degeneracy and the Limits of Edge-Colouring Techniques

## 2016 Fall Math Colloquia

September 21

Michael Schroeder (Marshall University)

A Survey of Graph Decompositions

October 24

Elizabeth Niese (Marshall University)

The combinatorics of symmetric polynomials

November 16

Scott Sarra (Marshall University)

Radial Basis Functions Methods and their Implementation

November 30

JiYoon Jung (Marshall University)

## 2016 Spring Math Colloquia

January 26

Avishek Mallick (Marshall University)

A Look at Permuatation (a.k.a. Randomization) Tests

February 24

Carl Mummert (Marshall University)

Incompleteness in mathematics

March 7

Shubhabrata Mukherjee (University of Washington, Seattle)

Introduction to Genetic Epidemiology in GWAS era

March 8

Shubhabrata Mukherjee (University of Washington, Seattle)

Genetic analyses of late-onset Alzheimer’s Disease

April 6

Anna Mummert (Marshall University)

## 2015 Fall Math Colloquia

September 2

Michael Schroeder (Marshall University)

Tournaments: Scheduling Them Fairly and More!

September 28

Nick Loehr (Virginia Tech)

Rook Theory 101

September 29

Nick Loehr (Virginia Tech)

Sweep Maps and Bounce Paths

October 21

Micheal Otunuga (Marshall University)

Stochastic Modeling of Energy Commodity Spot Price Processes

November 4

Martha Yip (University of Kentucky)

Coloring: the Algebraic Way

## 2015 Spring Math Colloquia

February 4

Elizabeth Niese (Marshall University)

What do trigonometry and combinatorics have to do with each other?

February 17

David Cusick (Marshall University)

350 Years of Service … and Then Pffft!

March 4

Gregory Moses (Ohio University)

Clustering and Stability of Cyclic Solutions in the Cell Division Cycle of Yeast

March 27–28

MAA Ohio Section Meeting at Marshall University

April 14

Judy Day (University of Tennessee)

Modeling the host response to inhalation anthrax to uncover the mechanisms driving risk of disease.

April 15

Judy Day (University of Tennessee)

Determining the what, when, and how of therapeutic intervention strategies for controlling complex immune responses.

## 2014 Fall Math Colloquia

September 3

Carl Mummert (Marshall University)

Is that a Prime Number?

September 17

Laura Adkins (Marshall University)

Interactive Regression Models with Centering

October 1

Michael Schroeder (Marshall University)

Latin squares and their completions

October 15

Xue Gong (Ohio University)

Clustering and Noise-Induced Dispersion in Cell Cycle Dynamics (No Link to Abstract)

November 5

Richard Brualdi (University of Wisconsin–Madison)

The Gale-Berlekamp Light-Switching Problem and a Permutation Variation

November 6

Richard Brualdi (University of Wisconsin–Madison)

All Things Bruhat: Matrix Bruhat Decomposition, Complete Flags, Bruhat Order of Permutations, (0,1) and Integral Matrices, and Tournaments

November 19

Bismark Oduro (Ohio University)

Designing Optimal Spraying Strategies for Controlling Re-infestation by Chagas Vectors

## 2014 Spring Math Colloquia

March 10

Jeffry L. Hirst (Appalachian State University)

Alan and Ada’s Theoretical Machines

March 11

Jeffry L. Hirst (Appalachian State University)

Reverse Mathematics, Graphs, and Matchings

April 9

JiYoon Jung (Marshall University)

The topology of chain selected complexes of a poset PDF

April 11

Lingxing Yao (Case Western Reserve University)

Mathematical Modeling and Simulation for Biological Applications

April 14

Stephen Flood (University of Connecticut – Waterbury)

Path, trees, and the computational strength of a packed Ramsey’s theorem

## 2013 Fall Math Colloquia

October 2

Lynne Yengulalp (University of Dayton)

Topological completeness

October 30

Roger Estep (Marshall University)

Filtered leapfrog time integration with enhanced stability properties

Robert Hughes (Marshall)

Agent-based modelin of pandemic influenza

November 18

Thomas Mathew (University of Maryland-Baltimore County)

The Assessment of Bioequivalence: A Statistical Overview

November 19

Thomas Mathew (University of Maryland-Baltimore County)

Methodology and Some Applications

## 2013 Spring Math Colloquia

January 30

Elizabeth Niese (Marshall)

A family of Catalan objects

February 20

Anna Mummert (Marshall)

Unit costs in optimal control of epidemics

April 24

Carl Mummert (Marshall)

If 1+1=9, does 2+2=7?

## 2012 Fall Math Colloquia

October 3

John Drost (Marshall)

What is Strategic Voting and What Can Be Done About It?

## 2012 Spring Math Colloquia

January 25

Michael Schroeder (Marshall)

Cyclic Matching Sequencibility of Graphs

Feburary 22

Anna Mummert (Marshall)

Studying the recovery procedure for the time-dependent transmission rate in epidemic models

March 7

Matthew Sedlock (Johns Hopkins University)

Percolation models

March 9

Avishek Mallick (University of New Hampshire)

Inferential procedures based on samples with nondetects from normal and related distributions

March 12

Myung Soon Song (University of Pittsburgh)

An unconventional approach to likelihood of correlation matrices

April 2

Sharad Silwal (Kansas State University)

Image quality assessment methods

April 6

JiYoon Jung (University of Kentucky)

The topology of restricted partition posets PDF

## 2011 Fall Math Colloquia

November 8

Carl Mummert (Marshall)

Two examples from infinitary combinatorics

## 2011 Spring Math Colloquia

April 5

Suman Sanyal (Marshall)

Stochastic Dynamic Equations

April 8

Elizabeth Niese (Virginia Tech)

Macdonald polynomials and the hook-length formula for standard Young tableaux

April 15

Andrew Oster (École Normale Supérieure)

A laminar model for the development of the primary visual cortex

April 18

Michael Schroeder (University of Wisconsin-Madison)

Phi-symmetric Hailton cycle decompositions of graphs

April 20

Remy Friends Ndangali (University of Florida)

Bound states in the radiation continuum and nonlinear effects in photonic structures

April 22. Paul Shafer (Cornell)

Coding arithmetic in the Medvedev degrees and its substructures

## 2010 Fall Math Colloquia

September 8

Anna Mummert (Marshall)

Get the News Out Loudly and Quickly: Modeling the Influence of the Media on Limiting Infectious Disease Outbreaks

October 13

Carl Mummert (Marshall)

The axiom of choice in mathematics and computability

November 9

Suman Sanyal (Marshall)

Stochastic Process Indexed by Time Scale

## 2010 Spring Math Colloquia

February 10

Anna Mummert (Marshall)

Parameter sensitivity analysis for mathematical modeling

April 14

Suman Sanyal (Marshall)

Stochastic dynamic equations and their applications

April 21

John Drost (Marshall)

Inheritance, bankruptcy, and the Talmud

## 2009 Fall Math Colloquia

September 16

Carl Mummert (Marshall)

Gaming around with topology

October 15

Sydney Thembinkosi Mkhatshwa (Marshall)

Super-spreading events

November 11

Duane Farnsworth (Marshall)

Approximation Numbers and Ideals of Operators

## 2006 Fall Math Colloquia

October 19

Peter Saveliev (Marshall)

Low level vision through topological glasses

## 2005 Spring Math Colloquia

February 22

Norah Esty (University of California – Berkeley)

Topological Properties of Orbit Sets for Groups of Homeomorphisms

February 24

Elmas Irmak (Michigan State University)

Mapping Class Groups

March 3

Akhtar Khan (Michigan Technological University)

An inverse problem in elasticity

April 8

Judith Silver

Conics in Projective Geometry

April 22

Bonnie Shook

Topological Approaches to Fingerprint Identification

Nathan Cantrell

Cubical Homology in Medical Imaging

April 29

Arthur Porter (Professor Emeritus, University of Toronto)

Manchester University’s Contributions to Analog and Digital Computing

## 2004 Fall Math Colloquia

September 24

Alfred Akinsete

The winning probability and ranking models for teams in soccer tournaments

October 8

Ralph Oberste-Vorth

From Chaos to Stability: Dynamic Equations Parameterized by Time Scales PDF

October 22

John L. Drost

What is the opposite of a prime number?

November 5

Elizabeth Duke and Kelli Hall

Time Scale Calculus and Dynamical Systems

November 19

Christopher Johnson and Peter Saveliev

Topological Proteomics: Pure Mathematics in Life Sciences

## 2004 Spring Math Colloquia

January 23

Yulia Dementieva

Statistical approaches to gene mapping

February 6

Linda Hamilton

Robotics of the Mars Station Program

February 19

Basant Karna (Baylor University)

Eigenvalue Comparison for Multipoint Boundary Value Problems

February 24

John (Matt) Matthews (Duke University)

Granular Materials: An Introduction & Application to Hopper Flows

February 27

Mohamed Elhamdadi (University of South Florida)

On knot invariants

March 5

Scott Sarra

Scattered Data Approximation with Radial Basis Functions

April 2

John L. Drost

Arrow’s Theorem or Why we all just can’t get along

## 2003 Fall Math Colloquia

September 26

John L. Drost

Addition Chains

October 10

Peter Saveliev

From slot machines to topology through calculus

October 24

Kelli Hall

Escher’s Tilings and Ribbons

November 7

Judith Silver

The Spherical Metric Project

December 5

Bonita Lawrence

Time Scales: A Snappy Link between Continuous Processes and Discrete Processes