# 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!

In Spring 2021, all talks will be scheduled from 2:30-3:30pm and will be held virtually
in Microsoft Teams**.**

**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.