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. For upcoming Math Colloquia please see the Department of Mathematics Events Calendar.

### 2020 Fall Math Colloquia

**September 16** Virtual, 4:00pm

Carl Mummert (Marshall University)

A case study in computable graph theory: König’s edge coloring theorem

*Abstract* Computable graph theory is a subfield of combinatorics and logic. A graph, in this sense, has a set of vertices (points), some of which are connected with edges. Graphs are applied to model many kinds of relationships in numerous disciplines. Computability theory uses a framework originally developed by Alan Turing to study the problems computers are theoretically able to solve. This talk will introduce computable graph theory using a specific theorem. König’s edge coloring theorem gives a way to assign colors to the edges of a graph using the least number of colors possible. I will introduce the theorem and many results about its computability theoretic properties.

No prior familiarity with graph theory or computability is needed, and this talk is aimed at a general audience.

**October 21** Virtual, 4:00pm

Michael Otunuga (Marshall University)

Time Dependent Probability Density Function for Number of Infection in a Stochastic SIS Epidemic Model

*Abstract:* The closed-form time dependent probability density function of the number of infected individuals at a given time satisfying a stochastic Susceptible-Infected-Susceptible (SIS) epidemic model is derived and analyzed using the Fokker-Planck equation. The mean, median, variance, skewness and kurtosis of the distribution are obtained as a function of time. We study the effect of noise intensity on the distribution and later derive and analyze the effect of changes in the transmission and recovery rates of the disease. The result is applied using published Covid-19 data/parameters.

**November 18** Virtual, 4:00pm

Michael Schroeder (Marshall University)

The null space of maximum density ASMs

*Abstract:* At some point in your life, you have been asked to “set it equal to zero and solve.” This is another such time. A large field of research is dedicated to computing the *spectrum* of a matrix, which in part asks the question,

If *A* is a matrix, for what vectors **x** does *A* **x** = **0**?

The set of all solutions to this equation is the *null space* of *A*. In this talk, we look at a particular family of matrices called *alternating sign matrices* (or ASMs for short), which are matrices with only 0s, 1s, and -1s in it that satisfy a certain “alternating” condition.

We define and describe some properties of maximum density ASMs, then compute their null spaces. Surprisingly, some elementary graph theory was helpful to solve the problem. This research is joint work with Pauline van den Driessche, from the University of Victoria.

Having some background in linear algebra would be beneficial, but the only requirement is that, at some point in your life, you’ve been asked to set something equal to zero and solve.

### 2020 Spring Math Colloquia

**February 19** Smith Hall 516, 4:00pm

Alaa Elkadry (Marshall University)

Inference when Data Sources Uncertain

*Abstract:* Data with uncertain sources are available all around us. Specifically, we’re talking about the cases where each observation has a probability distribution. Randomized response data and assessing possible landing disparity are among the application areas of such data.

In this talk, examples of some application areas are further discussed, and illustrative examples are provided to demonstrate the calculations for each case discussed.

### 2019 Fall Math Colloquia

**September 18** Smith Hall 516, 4:00pm

Faith Hensley (Marshall University)

Extremal Numbrix Puzzles

*Abstract:* Numbrix is a puzzle in Parade magazine. The player is given a 9 × 9 grid with some integers between 1 and 81 filled in. The player then needs to fill in the rest of the integers between 1 and 81 so that consecutive integers appear in adjacent cells of the grid. Generalizing this puzzle we consider m × n grids with the entries being the integers between 1 and mn. We say that a set of clues defines a puzzle if there exists a unique solution given those clues. In 2018 Hanson and Nash find the maximum number of clues that fail to define an m × n puzzle for all m and n. I present our work on their conjecture concerning the minimum number of clues necessary to define a puzzle. This research is joint work Ashley Peper conducted as part of the 2019 REU program at Grand Valley State University.

Chloe’ Marcum (Marshall University)

Extended Schur Functions

*Abstract:* The set of quasisymmetric functions homogeneous of degree n form a polynomial

vector space, *QSym*, with multiple bases. Many of these bases can be generated

combinatorially using tableaux with various rules. The bases of *QSym* we are interested

in are the quasisymmetric Schur functions and the extended Schur functions.

Both generalize the symmetric Schur functions. A common question in linear algebra

is how to transition from one basis to another. We have an expansion of

extended Schur functions into quasisymmetric Schur functions for a family of indexing

compositions. We prove this expansion combinatorially by using a tree

whose leaves indicate the polynomials that appear in our expansion.

**October 16** Smith Hall 516, 4:00pm

Logan Rose (Marshall University)

Modeling Malaria with Controls

*Abstract:* Malaria is a deadly parasitic disease that has been a major threat to public health for centuries, particularly in Sub Saharan Africa and South Asia. Although there are still 200 million cases reported yearly according to the CDC, there have been renewed efforts in recent decades to combat this illness. Mathematicians have created various models using differential equations to simulate the spread of malaria and to determine which control strategies are most effective in reducing the number of new infections. Many of these consider the interactions between humans and the Anopheles mosquito, the primary vector of the disease. This project considers the effectiveness of two popular malaria control strategies: using bednets and releasing sterile mosquitoes. We used an eight-equation model that combines an SEIR (Susceptible-Exposed-Infected-Recovered) model for the human population, an SEI (Susceptible-Exposed-Infected) model for the vector population, and an additional equation for the sterile mosquito population. In addition, we applied the Next Generation Matrix method to our model to derive a formula for the basic reproduction number for infectious disease. Finally, we apply optimal control theory to find the optimal releasing strategies, and numerical simulations are presented for various cases.

Michael Waldeck (Marshall University)

Generalizing the Classical Construction for Complete Sets of Mutually Orthogonal Latin Squares

*Abstract:* Latin squares are a well established topic of study in Mathematics. A latin square of size n is an n by n square where each number from 1 to n appears exactly once in each row and in each

column. Two latin squares are orthogonal mates if, when the squares are superimposed, every

possible ordered pair of entries appears in the superimposed square. In the 18th century, Leonhard

Euler studied the question of finding a complete set of mutually orthogonal latin squares (MOLS)

of a given size. Euler proved that for each n, a set of n by n MOLS can have no more than n – 1

squares. It has also been proved that, where n is a prime power, this upper bound is achieved

through the classical construction. The classical construction for a complete set of MOLS of size

n by n can be given by a formula M(i, j) = i + cj, where c is a nonzero element in the finite field of order n. We study the number of orthogonal mates and the graph of the mate relationship between a family of latin squares based on a generalization of that formula. That is, when q is prime, we study the set of latin squares of size q by q that can be given by a formula S(s, c)(i, j) = s(i) + cj,

where s mapping the finite field of order q to itself is a permutation of the field, c is a nonzero element in the finite field of order q, and the addition and multiplication are carried out in the finite field.

**November 20 ** Smith Hall 530, 4:00pm

Carl Mummert (Marshall University)

How to Multiply Big Natural Numbers

*Abstract:* Big natural numbers are all around. They keep your data private on the internet, and scientists use them for high precision simulations. Adding big numbers is not very hard, but multiplying them is much more challenging. The problem of multiplying numbers efficiently is at the border between mathematics and computer science.

I will introduce several multiplication algorithms currently used in state of the art software. Then I will describe a breakthrough announced by two researchers in March 2019. They produced an algorithm that can multiply two natural numbers – of any size – with an efficiency we think is optimal. This talk is aimed at anyone with a background of college algebra or higher.

### 2019 Spring Math Colloquia

**March 20**

Jiyoon Jung (Marshall University)

Enumeration of Fuss-Schroder paths by types and connected components

Smith Hall 516, 4:00pm

*Abstract:* Catalan numbers form a sequence of natural numbers that occur in various important counting problems in Combinatorics. Dyck paths are one of the problems that engaged Catalan numbers. In this talk, the applications of Dyck paths are introduced by considering types of paths, connected blocks, Schroder paths, and Fuss analogues.

**April 17**

Michael Schroeder (Marshall University)

Putting Numbers in Grids: Theory and Applications

Smith Hall 516, 4:00pm

*Abstract:* There are many games that involve putting numbers in a grid, like Sudoku, but there are equally many theoretical and practical applications for putting numbers in a grid. Grids with certain conditions met, like no numbers repeated in a row or column, have uses in cryptography, statistics, and experimental testing.

In this talk, we begin with an introduction to Latin squares (a grid of numbers meeting certain Sudoku-like conditions) and discuss a few of their many applications. We then look at some embedding problems (completely filling a partially filled grid with certain conditions) and discuss some recently published results in this area.

You may not improve your Sudoku-solving skills by attending this talk, but you should gain some appreciation for why such games can be useful in the real world!

This is a talk for a general audience! Tell your friends!

### 2018 Fall Math Colloquia

**September 19**

Elizabeth Niese (Marshall University)

The RSK algorithm and applications

Smith Hall 516, 4:00pm

*Abstract:* The Robinson-Schensted-Knuth (RSK) algorithm is a classical algorithm in algebraic combinatorics. It is a bijection between words and pairs of tableaux which has many interesting combinatorial properties. There are a number of distinct constructions equivalent to this algorithm, including the jeu-de-taquin and Viennot’s shadow lines construction. We will look at several of these constructions and their use in proofs of algebraic formulas.

**October 17**

Chloé Marcum (Marshall University)

Using polynomials to study knots

Smith Hall 516, 4:00pm

*Abstract:* A knot is any closed loop in space. Two knots may be the same knot even though they appear to be different. A local move is a change to a small portion of a knot and the rest of the knot is assumed to stay the same. A local move may or may not change the knot. An invariant is a characteristic of a knot that help us tell the difference between knots. In our research, we studied certain polynomials that are knot invariants. We studied the effect of certain local moves on Homflypt and Kauffman polynomials. As a consequence, we discovered some new properties of these invariants.

This research was completed in summer 2018 as part of a Research Experience for Undergraduates (REU) at St Mary’s College of Maryland. At the end of the talk, I will share general information about REUs as well as my experience at St. Mary’s.

Knot theory is an area of math that is understandable without a lot of math background. All students interested in math are encouraged to attend.

**November 28**

Raid Al-Aqtash (Marshall University)

Market Basket Analysis

Smith Hall 516, 4:00pm

*Abstract: *Market basket analysis is a data mining technique based upon using association rules to uncover the purchasing trends in large transaction datasets. The key factor here is to determine possible lists of items that are frequently sold together. In this talk, I will speak about association rules and how they can be used by large retail companies in market basket analysis. A real dataset will be provided in an application of association rules.

Keywords and phrases: *data mining, basket analysis, beer and diapers, association rules, support, confidence, lift.*

This will be a general audience talk, using a bit of information about proportions and percentages.

### 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