# Faculty Research Spotlight

The Faculty Research Spotlight is intended to introduce students to Department of Mathematics faculty research interests, but everyone is welcome to attend!

**Upcoming Events**

**No events currently scheduled**

## Past Events

#### Monday, August 31, 2020

**SPEAKER: Dr. Sarah Holliday****RESEARCH AREA:**Graph Theory**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"Graph Designs; from cookie baking to ship captains"***ABSTRACT:**We can use techniques from the intersection of graph theory and design theory to solve problems in the area of scheduling and experimental design. I've been working on a variant of one problem for many years, and while I have made some impressive strides over the years, there is still a great deal of work to be done.

#### Monday, September 14, 2020

**SPEAKER: Dr. Andy Wilson****RESEARCH AREA:**Combinatorics/Algebra**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"The mathematics of voting districts"***ABSTRACT:**The US House of Representatives consists of 435 voting members, each representing a district. Each state is allocated a certain number of districts based on its population. There are surprisingly few legal restrictions on how these districts can be drawn, allowing officials to sometimes draw "unfair" maps that are usually called "gerrymanders." In recent years, mathematicians have developed several methods for detecting and avoiding gerrymanders. I will give an overview of some of these methods, which involve techniques from graph theory and probability, and discuss open problems in this area.

#### Monday, September 28, 2020

**SPEAKER: Dr. Eric Stachura****RESEARCH AREA:**Partial Differential Equations**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"Differential equations in Electromagnetism"***ABSTRACT:**Differential equations are useful to study many natural phenomena. In this talk, I will discuss differential equations which arise in Electromagnetism. In particular, I will show how scattering of Electromagnetic waves by obstacles has applications to radar surveillance and medical imaging, among many other areas. I will then introduce Geometric Optics and pose an optical refraction problem, where we will see nonlinear differential equations appear. Finally, I will address an issue in Electrical Engineering (Passive Intermodulation) which is important for the design of modern communication systems. I will end with some open problems and some differential equations in other physical contexts, including quantum mechanics and electromechanics.

#### Monday, October 12, 2020

**SPEAKER:**Dr. Tsz Ho Chan**RESEARCH AREA:**Number Theory**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"Close Factors of an Integer"***ABSTRACT:**Consider the number*n*= 99990000. It can be factored as*n*= 9999 * 10000 = 9900 * 10100 with 4 factors close to its square root.

Can an integer*n*have many factors close to its square root? What do we mean by "many" and what do we mean "close"?

In this talk, we will explore this and other related questions. For example, it turns out that perfect squares 1, 4, 9, 16, … can have at most five factors "close" to its square root.

#### Monday, October 26, 2020

**SPEAKER: Dr. Pengcheng Xiao****RESEARCH AREA:**Mathematical Biology**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"Hypothalamus-pituitary-adrenal axis (HPA) modeling introduction"***ABSTRACT:**The human stress response is controlled largely by the hypothalamic-pituitary-adrenal (HPA) axis. Models predicting the levels of the hormones involved are very often not analytically solvable because of nonlinear complexity. In this talk, we will review the recent developments in this area.

#### Monday, March 22, 2021

**SPEAKER: Dr. Thomas McConville****RESEARCH AREA:**Combinatorics**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"Unimodal sequences and a conjecture of Morier-Genoud and Ovsienko"***ABSTRACT:**A finite sequence is unimodal if it increases up to a point, then decreases afterward. Unimodal sequences abound in Mathematics, appearing in counts of subsets, unlabeled graphs, partitions, triangulations, and other fundamental structures. In this talk, I will showcase a few common techniques to prove unimodality and present a recent conjecture that has resisted all attempts at proof so far. Part of this talk is based on joint work with Bruce Sagan and Clifford Smyth.

#### Monday, March 29, 2021

**SPEAKER: Dr. Yizeng Li**(Assistant Professor of Mechanical Engineering at KSU)**RESEARCH AREA:**Cell Mechanics and Mechanobiology**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"Using a two-phase fluid model as a mathematical tool to study mammalian cell migration"***ABSTRACT:**Mammalian cell migration is important in wound healing, immune response, tissue regeneration, morphogenesis, and cancer metastasis. Multiple biophysical processes are involved in cell migration and the mathematical modeling of these processes provides an interesting insight into some fundamental mechanisms. In this talk, I will begin with an introduction to the physics and biology of mammalian cell migration under different environments. I will then introduce a two-phase fluid model of cell migration by considering various biophysical conditions that surround a cell. Emphasis will be given on how to develop conservation laws and boundary conditions for the model. In the end, I will discuss several non-trivial model predictions that have implications on in vivo cell migration.

#### Monday, April 5, 2021

**SPEAKER:****Dr. Julie Vega****RESEARCH AREA:**Combinatorics**TIME/LOCATION:**2:30-3:30pm online in Microsoft Teams**TITLE:***"t-stack sortable permutations on the permutahedron"***ABSTRACT:**The permutahedron is an (n-1)-dimensional polytope whose vertices are the permutations of the first n natural numbers with edges between two vertices if and only if they differ by a transposition. To each permutation we can assign a value t which tells us how many times a permutation needs to go through the Stack-Sorting Algorithm (originating from computer science) before it becomes the identity permutation. Our main goal for this project will be to consider how the permutahedron, and other orbit polytopes, "decompose" over t-stack sortable permutations. This project is ongoing work with Andrés Vindas Melendéz.

#### Monday, September 27, 2021

**SPEAKER:**Dr. Asma Azizi**RESEARCH AREA:**Mathematical Biology**TIME/LOCATION:**2:00-3:00pm, location D-225**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Socio-Ecological Application of Mathematical Models — Two epidemiological metaphors"***ABSTRACT:**A mathematical model is a mathematical representation of a real-world situation. It simplifies real-world problems for describing an event, making predictions, and understanding complex relationships. Mathematical models have long been a common tool to understand biological systems and particularly, played a prominent role in understanding and predicting spread of infectious diseases. The diversity of purpose and application of mathematical models used in biological and epidemiological systems offer of their great potential for understanding a wide range of topic in social sciences. Social sciences usually study human society and social interactions. Indeed, it's a vast field of study and includes a multitude of study areas. In this talk, we will explore the use of mathematical models in such areas via two examples: homelessness issue and obesity as epidemics. The talk I present is the research conducted by undergraduate students who worked in a team to address these two social issues and measure their intensity using mathematical models.

#### Monday, October 4, 2021

**SPEAKER:**Jessie Chen (KSU math student)**RESEARCH AREA:**PDEs, computational mathematics, and optimization**TIME/LOCATION:**2:00-3:00pm, location D-225**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Ways to Enter Undergraduate Research and My Experiences Doing So"***ABSTRACT:**There are many ways to gain undergraduate research experience, such as reaching out to a familiar professor, attending departmental events, or participating in an REU. In this talk, I will briefly introduce three different research projects (2 with professors at KSU, one outside KSU) as well as how to get involved with undergraduate research and my experiences doing so. In addition to taking questions about each research topic, I will also answer questions on getting started in undergraduate research.

#### Monday, October 25, 2021

**SPEAKER:**Nick Hancock (KSU engineering student)**RESEARCH AREA:**Mathematical Physics**TIME/LOCATION:**2:00-3:00pm, location D-225**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"A Mathematician and an Engineer Walk into a Bar: An Interdisciplinary Study in Quantum Physics"***ABSTRACT:**In a previously published work, a new type of screened Coulomb potential was introduced within the context of Time-Dependent Density Functional Theory in order to satisfy the Runge-Gross Theorem. The Hellman-Feynman and Hypervirial Theorems, variational principle, and extended Nikiforov-Uvarov method are employed to study properties of solutions and the number of bound states for the Schrodinger equation of a Hydrogen atom with this potential. This is work with Dr. Stachura.

#### Monday, November 8, 2021

**SPEAKER:**Christopher Boon (KSU math student)**RESEARCH AREA:**Mathematical Biology**TIME/LOCATION:**2:00-3:00pm, location D-225**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Why be excited about research?"***ABSTRACT:**Undergraduate research is a unique opportunity that can offer the student many benefits. Typical research skills include information searching and discovery by linking ideas. Outside of these hard research skills, students can earn course credit, earn scholarships, and develop mathematical maturity. In addition, I discuss my experience throughout a long-term project on modeling of cell migration, my expectations going into research, unexpected benefits, and what I would do differently if I were to conduct research again.

#### Monday, January 31, 2022

**SPEAKER:**Dr. Tim Faver**RESEARCH AREA:**Analysis / Partial Differential Equations (PDE)**TIME/LOCATION:**3:00-4:00pm, location D-250**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Nonlinear Waves in Fermi-Pasta-Ulam-Tsingou Lattices"***ABSTRACT:**Infinite chains of coupled oscillators model a diverse array of physical phenomena. Simultaneously, their governing equations exhibit surprising mathematical behavior as certain key parameters are tweaked and varied. I will discuss the dynamics of one such chain, the Fermi-Pasta-Ulam-Tsingou lattice, and suggest some of the deep analytical questions that arise from seemingly trivial observations about its material structure.

#### Monday, February 14, 2022

**SPEAKER:**Dr. Tsz Chan**RESEARCH AREA:**Number Theory**TIME/LOCATION:**3:00-4:00pm, location D-250**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Gaps Between Squarefree Numbers"***ABSTRACT:**An integer is squarefree if it is not divisible by any perfect square greater than 1. For example, 15 is squarefree but 16 is not. So, the initial list of squarefree numbers is: 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, ... In this talk, we will talk about spacings between squarefree numbers and highlight some ideas involved in its study. They include geometry of curves, differencing techniques and Taylor series.

#### Monday, February 28, 2022

**SPEAKER:**Dr. Sean Ellermeyer**RESEARCH AREA:**Game Theory**TIME/LOCATION:**3:00-4:00pm, location D-250**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Should we Have an Auction or a Raffle?"***ABSTRACT:**A wealthy donor has just donated a brand new Harley-Davidson motorcycle to our KSU Math Enthusiasts student club. We don’t have any need for the motorcycle itself so we decide that we should use it to raise money for our club to be able to host guest speakers, fund student travel to math conferences and do other fun things. One possible way to sell the motorcycle would be to hold an auction. Another possible way would be to hold a raffle. Which way would be better? In this talk, we will see how Mathematics and Economics are combined (in particular through Game Theory) to address this question. We will highlight recent research on raffles in which we have obtained some interesting results but for which there are still open questions.

#### Monday, March 14, 2022 — SPECIAL PI DAY TALK

**SPEAKER: Dr. Andy Wilson****RESEARCH AREA:**Combinatorics/Algebra**TIME/LOCATION:**3:00-4:00pm, location D-250**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"A talk approximately about pi"***ABSTRACT:**How can we estimate the value of pi? Much effort has been spent on this problem throughout the history of mathematics. I will focus on one particular approximation that can be traced back to Madhava, a 14th century Indian astronomer, and this approximation's surprising connections to combinatorics and chemistry. Very little background will be assumed and I hope to make this talk approachable to anyone who wants to celebrate Pi Day!

#### Monday, March 28, 2022

**SPEAKER: Dr. Glenn Young****RESEARCH AREA:**Mathematical Biology and Dynamical Systems**TIME/LOCATION:**3:00-4:00pm, location D-250**Mathematics building, Marietta campus**and streaming online in Microsoft Teams**TITLE:***"Evolutionary game theory or: Wait, you can use math to study cooperation?"***ABSTRACT:**Why do we (or any living organisms) cooperate? Cooperation, the act of expending one's own energy or resources for the good of the group, is a necessary part of life, but is also exploitable by so-called "defectors" who choose not to help out yet still reap the benefits that cooperation yields. In fact, under fairly general assumptions, every rational individual will (theoretically) choose to defect, thereby extinguishing cooperation and dooming society. Of course, cooperation has not been extinguished and is in fact quite common in the natural world. This observation brings us back to the question posed at the beginning of this abstract. In this talk, I will discuss a mathematical framework through which cooperation is often studied called evolutionary game theory and present several classic and recent results from the field.