## Faculty Talks Session Index

Click a session title to jump to the abstracts.

Faculty Session I

1:20-2:11, BPMC 208

Speakers: Guoan Diao, Allison Kolpas

Faculty Session II

1:20-2:11, BPMC 210

Speakers: Eva Goedhart, Lin Tan

Faculty Session III

1:20-2:11, BPMC 211

Speakers: Chuan Li, Asif Mahmood, Baoling Ma

Faculty Session IV

1:20-2:11, BPMC 212

Speakers: Samantha Pezzimenti, Wing Hong Tony Wong, Garth Isaak

## Faculty Session I

BPMC 208

1:20pm, **Guoan Diao** (Holy Family University)

*On the sum of squares of consecutive integers*

View Abstract

One algebra problem drew my attention: Find two and three consecutive integers such that 365 can be expressed as the sum of two consecutive integer squares and also the sum of three consecutive integer squares. This is a good practice problem for College Algebra students. Can we find numbers other than 365 which also have this property? In this talk I will show you how to find these numbers, and explore some other related problems as well.

1:38pm, **Allison Kolpas** (West Chester University)

*Engaging undergraduate students in research in mathematical biology at WCUPA*

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I will discuss three different research projects in mathematical biology in which my collaborators and I have had success involving undergraduate students. The first research project was a collaboration with the laboratory of Dr. Frank Fish, professor of biology at WCUPA. The research involved analyzing the kinematics of swimming of manta-ray from video recordings. The other two research projects are part of an NSF RUI grant that I share with Dr. Josh Auld, an associate professor in the biology department at WCUPA. We have been analyzing experimental data and developing predictive optimization models to understand how environmental conditions (such as predation risk and mate availability) shape life-history expression and evolution in Physa acuta, a hermaphroditic species of freshwater snail. Our last two research projects resulted in publications co-authored by students in the Journal of Evolutionary Biology and the Bulletin of Mathematical Biology.

1:56pm, Canceled Talk

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## Faculty Session II

BPMC 210

1:20pm, **Eva Goedhart** (Lebanon Valley College)

*Using Continued Fractions to Solve Diophantine Equations*

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I will give a light review of simple continued fractions before showing how to use key continued fraction results to solve a family of Diophantine equations.

1:38pm, Canceled Talk

1:56pm, **Lin Tan** (West Chester University)

*A Hybrid local-global approach to solutions of some recursive relations*

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Solutions to a recurrence relations can be given ''globally'' by presenting its generating function, or ''locally'' by presenting its ''Binet Form''. We will present a hybrid approach that will give a more practical method for finding the general terms for some recurrence relations.

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## Faculty Session III

BPMC 211

1:20pm, **Chuan Li** (West Chester University)

*Modeling Electrostatic Potentials on Molecules and Proteins by a Differential Equation and Its Application in Biophysics*

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Electrostatic interactions, the only known long-range force to provide guidance of long distance, is among the most important factors to consider when analyzing the function of biological molecules and proteins. One of the most well-known models for simulating electrostatic potentials and various energy in biophysics is the Poisson-Boltzmann equation (PBE), which has been widely adopted in virtually any protein-related research effort. In this talk, I will present the formulation of the PBE, an iterative numerical method for solving the PBE on biomolecules, and its implementation in a scientific program called DelPhi. Biological simulation results are provided as well to demonstrate how Math models and methods are utilized in the real world for better understanding of the mother nature.

1:38pm, **Asif Mahmood** (Penn State York)

*Non-Newtonian power-law fluid flow in deformable porous media*

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We investigate the behavior of a spherical cavity in a soft biological tissue modeled as a deformable porous material during an injection of non-Newtonian fluid that follows a power law model. Fluid flows into the neighboring tissue due to high cavity pressure where it is absorbed by capillaries and lymphatics at a rate proportional to the local pressure. Power law fluid pressure and displacement of solid in the tissue are computed as function of radial distance and time.

1:56pm, **Baoling Ma** (Millersville University)

*A Mathematical Model for an Amphibian Population with Distributed Birth and Metamorphosis Rates*

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Habitat destruction, alteration and fragmentation, climate change, and pollution are most serious causes of amphibian population declines worldwide. Amphibian larvae respond to environmental changes by varying metamorphosis rate, or size at metamorphosis. A general mathematical model is developed where larvae may metamorphose into adult frogs of different sizes and at different rates. A finite difference scheme is developed to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. Numerical simulations are provided to understand the effects of distributed metamorphosis rates in an urban American green tree frog (Hyla cinerea) population.

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## Faculty Session IV

BPMC 212

1:20pm, **Samantha Pezzimenti** (Penn State Brandywine)

*Minimal Lagrangian Capping Genus*

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If a knot bounds a surface, it doesn't matter how that surface is positioned in space. The surface could lie above the knot (a cap) or below the knot (a filling). Just flip it upside down, right? However, if the knots are Legendrian and the surface is Lagrangian (meaning they satisfy some extra conditions coming from contact/symplectic geometry), this is not the case. In fact, if the Legendrian knot has a filling surface, it cannot have a capping surface! In this talk, I describe a method of minimizing the genus of a Lagrangian cap of a Legendrian knot.

1:38pm, **Wing Hong Tony Wong** (Kutztown University of Pennsylvania)

*On an Unconventional Graph Coloring Problem*

View Abstract

One of the primary purposes of graph coloring is to distinguish objects. In this project, instead of studying proper coloring of graphs, we focus on edge-distinguishing vertex coloring. After we color the vertices of a simple graph \(G\), we label each edge by the set of colors on both end vertices. If no two edges share the same label, then we say the vertex coloring is edge-distinguishing. We would like to find out the minimum number of colors we need for various graphs to achieve edge-distinguishing.

1:56pm, **Garth Isaak** (Lehigh University)

*Voting profiles, Discrete Tomography, Edge Coloring Bipartite Multigraphs, 3-Dimensional Contingency Tables, \(\ldots\)*

View Abstract

What do the items in the title have in common? They, or special cases of them all can be viewed as the Birkhoff-Von Neumann Theorem using different notation (although the graph coloring result came first). We will discuss these connections and how they might be motivated in a combinatorics, discrete math or proofs course. Finally we will discuss how the generalization, edge list coloring plays out in the different settings.

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