Session Index
Click a session title to jump to the abstracts.
Undergraduate Session 1
2:15pm--3:15pm, WBC 225
Speakers: Olivia Lutterodt, Aicha Konneh, Harlensky Nerett, Avinash Kaur, Lily Kochanowicz, Callie Buffaloe, Carley Sicilia, Olivia Domanico, Lacey DeAngelo, Jojo Jimenez, Savannah Flores
Undergraduate Session 2
2:15pm--3:15pm, WBC 304
Speakers: Addison Stanton, Emma Kaplan, Thomas Stauffer, Alessia Revelli
Undergraduate Session 3
2:15pm--3:15pm, WBC 310
Speakers: Kyle McCaffery, Nesty Dogbatse, Peter Palma, Paul McGinley
Undergraduate Session 4
2:15pm--3:15pm, WBC 314
Speakers: Onil Morshed, Alex Glatfelter, Evan Gibbs
Undergraduate Session 5
2:15pm--3:15pm, WBC 403
Speakers: Sean Funk, Kaden Hunter, Alexandra Ziegler, Peyton Haroldson, Kaden Hunter, Alexandra Ziegler, Peyton Haroldson, Nathan Tam
Undergraduate Session 6
2:15pm--3:15pm, WBC 404
Speakers: Lukas Walko, Mackenzie Carr, Daniel Cerra
Undergraduate Session 1
WBC 225
2:15pm, Olivia Lutterodt, Aicha Konneh (Saint Joseph’s University )
The prisoners and hats puzzle
View Abstract
The famous prisoner and hat logic puzzle was created by a number of mathematicians. This problem has been around since 1961 and has been rooted from game theory and epistemic logic. In our talk, we will discuss the history of our problem, the theories that were developed, and have the students try to solve it.
Close Abstract2:27pm, Harlensky Nerett, Avinash Kaur, Lily Kochanowicz (Saint Joseph's University )
Sophie Germain: A Pioneer for Women in Mathematics
View Abstract
Sophie Germain was a French mathematician who overcame difficult obstacles as women to make significant contributions to the field of mathematics. She helped create key methods for the way to approach Fermat’s Last Theorem, and she brought key ideas that influenced mathematicians. This presentation will talk about her life, the obstacles she had to overcome, and groundbreaking work on the lasting influence in the field of mathematics.
Close Abstract2:39pm, Callie Buffaloe, Carley Sicilia (Saint Joseph's University )
The Life of Sofya Kovalevskaya
View Abstract
Sofya Kovalevskaya was the first woman in the world to earn a doctorate in mathematics. She had groundbreaking research in partial differential equations and mechanics, which helped establish the Cauchy-Kovalevskaya theorem. Sofya was a professor at the University of Stockholm, and served as an editor of the mathematics journal, Acta Mathematica. Our presentation will highlight her work, while also advocating for other women in education.
Close Abstract2:51pm, Olivia Domanico, Lacey DeAngelo, Jojo Jimenez (Saint Joseph's University)
Ada Lovelace
View Abstract
Augusta Ada Byron King, better known as Ada Lovelace, is a British mathematician from the early to mid-1800s. She was one of the first women to use “computers” in mathematics by writing algorithm code long before modern computers were in existence. Our presentation will discuss Ada’s findings and legacy in the world of mathematics, while also briefly touching on her personal life.
Close Abstract3:03pm, Savannah Flores (Saint Joesph Univeristy)
The Biography Of Grace Hopper
View Abstract
Back to index
Undergraduate Session 2
WBC 304
2:15pm, Addison Stanton (Penn State Brandywine)
Residue Diagrams and String Art
View Abstract
Using these straight lines connecting a series of points as building blocks, intricate and elaborate designs can be created, all with deep mathematical connections. For instance, connecting opposite pairs of points along the legs of any angle creates the tangent space of a parabolic curve. By arranging points evenly spaced on a circle, we can exhibit properties of number theory, abstract algebra, and trigonometry. In this presentation, we will focus on residue diagrams, which form the tangent space of polar curves such as cardioids by connecting points in a particular way. We will also present a large-scale art installation depicting a 14-ft diameter residue diagram in the desert.
Close Abstract2:30pm, Emma Kaplan (Penn State Brandywine)
Cylindrical and Mobius Knot Mosaics
View Abstract
Knot projections can be constructed out of a set of specific mosaic tiles arranged in a square grid. This allows us to define knot invariants such as the mosaic number, or the minimal size grid needed to build the knot with tiles. In this project, we consider identifying a pair of edges of the square to form mosaics on either a cylinder or a Mobius band. We define the cylindrical and Mobius mosaic numbers and explore some computational bounds on these invariants. We will share some work in progress as well as some open questions that can extend this project further.
Close Abstract2:45pm, Thomas Stauffer (Penn State Brandywine)
Making Music with Knot Theory
View Abstract
Aspects of music theory can be understood via group theory in a surprisingly visual way. Chord progressions following the functions of Neo-Riemannian music theory can be viewed as a path along a generalized version of Waller's torus, inspired by the musical Tonnetz, first introduced by Euler. We can analyze such paths that form torus knots and explore infinite sequences of torus knots that can be expressed via the same song. I will perform some examples of these knotted progressions!
Close Abstract3:00pm, Alessia Revelli (Susquehanna University )
Connectivity of Grouped Stirling Complexes
View Abstract
Given a graph $G$, a Stirling Complex can be viewed as the set of all configurations of robots which can move along $G$, provided there is at least one robot on each vertex of $G$. In this talk, we will introduce a variation of Stirling Complexes called Grouped Stirling Complexes in which we place the robots into groups, and no two robots from the same group can occupy the same location on $G$. We will focus on the connectivity of these spaces and show we can move between any two configurations, provided there is at least three groups.
Close AbstractBack to index
Undergraduate Session 3
WBC 310
2:15pm, Kyle McCaffery (Monmouth University)
Using the Theory of Quantum Graphs to Analyze Star Graphs with an Infinite Count of Connected Strings
View Abstract
It is well known that the harmonics of a singular string may be represented by
\[
k = \frac{n \pi}{L}
\]
where $n$ is an integer and $L$ is the length of the string. This concept can also be easily applied to studying the harmonics of two strings. Joining two strings at a central node acts similarly to one string that is of a greater length. Thus, we can simply state the following
\[
k = \frac{n \pi}{L_1+L_2}
\]
where $L_1$ and $L_2$ are the lengths of our two strings. We do not, however, have a similar luxury when it comes to string counts greater than 2. When we have more than 2 strings that meet at a central node, the strings form a star shape, as opposed to one longer string like in the previous case. We will consider a star graph that has a countably infinite number of strings that are joined together by a single, central node. We will use the theory of quantum graphs to analyze this graph to determine if there is some general means to represent graphs of this nature, as well as their harmonics.
Close Abstract2:30pm, Nesty Dogbatse, Peter Palma (Villanova University)
Arithmetical structures on cycles with a multiedge
View Abstract
An arithmetical structure on a graph is an integer labeling on the vertices of
the graph such that the label at each vertex divides the sum of the labels of its
neighbors and the gcd of the labels is 1. Dino Lorenzini originally defined them
in order to answer some questions in algebraic geometry, but more recently,
they have been studied on their own, particularly through a combinatorial lens.
In this talk, we discuss enumerative results related to arithmetical structures
on cycles with a multiedge.
Close Abstract2:45pm, Paul McGinley (Villanova University)
Spectral Radii of Arithmetical Structures on Broom Graph
View Abstract
An arithmetical structure on a graph is an integer labeling on the vertices of the graph such that the label at each vertex divides the sum of the labels of its neighbors and the gcd of the labels is 1. Dino Lorenzini originally defined them to answer some questions in algebraic geometry, but more recently, they have been studied on their own, particularly with a combinatorical and algebraic lens. In this talk, we will discuss results on the spectral radius of some matrices associated with these structures, with a specific emphasis on arithmetical structures on broom graphs.
Close AbstractBack to index
Undergraduate Session 4
WBC 314
2:15pm, Onil Morshed (Gettysburg College)
Automated Apple Variety Classification Using Machine Learning for Industrial Applications
View Abstract
Manual classification of apple varieties is labor-intensive and error-prone, hindering efficiency in high-throughput fruit processing. This study evaluates four machine learning models-K-Nearest Neighbors (KNN), Support Vector Machines (SVM), Random Forest, and ResNet-50-on the Fruit-360 dataset subset with 23 apple varieties. Performance is assessed using testing accuracy, macro-average F1-score, weighted-average F1-score, and computational efficiency. ResNet-50 achieves the highest testing accuracy of 99.6% and F1-score of 0.99. On the other hand, SVM follows with 98.6% accuracy and 0.99 F1-score, while Random Forest and KNN achieve 95.6% and 91.5% accuracy, respectively. SVM is recommended for its balanced accuracy and runtime, suitable for Rice Fruit Company's industrial needs, while highest accuracy of ResNet-50 is limited by its 8x higher runtime than SVM.
Close Abstract2:30pm, Alex Glatfelter (York College of Pennsylvania)
Dynamics of Voter Satisfaction and Political Party Polarization in Electoral Systems: A Mathematical and Simulation Based Approach
View Abstract
This project analyzes how ideological changes in individuals and political parties affect voter satisfaction and party polarization. We set up a theoretical, simulation-based two-dimensional ideological trait space to represent both voters’ and parties’ ideologies. Within this space, individuals update their positions based on their prior ideology, peer influence, media exposure, party alignment, and random shocks capturing misinformation, biases, and irrationality. Parties adjust their platforms based on their prior ideology, responsiveness to their base, strategic positioning relative to rivals, and stochastic shocks capturing the same forces. These update equations jointly determine the evolution of ideological positions over time. Voter satisfaction is calculated as a function of ideological distances between individuals and party platforms and the relative size of each party. We hypothesize that when seat allocation is roughly proportional to voter identification, average satisfaction will rise as the number of viable parties increases, whereas in systems that over-reward large parties, satisfaction will tend to fall as the number of parties increases. Finally, initial conditions strongly influence the system’s evolution, with dynamics either converging toward moderation or diverging toward polarization. Results are preliminary; future work calibrates the model to data and conducts robustness checks.
Close Abstract2:45pm, Evan Gibbs (York College of Pennsylvania)
Optimal Control Approach to Developing Sex-Structured Release Strategies For Dengue Prevention
View Abstract
Dengue fever is a mosquito-borne viral infection prevalent in tropical and subtropical regions, placing nearly half of the global population at risk. Transmission occurs primarily through bites of infected female Aedes aegypti and Aedes albopictus mosquitoes, resulting in over 100 million infections annually. Consequently, effective disease and vector control are of the utmost importance. Wolbachia, maternally transmitted endosymbiotic bacteria found in roughly 60% of arthropod species, have emerged as a promising biological control strategy. By reducing mosquito fitness and fertility, and by inducing cytoplasmic incompatibility, Wolbachia can suppress dengue transmission.
In this work, we analyze a sex-structured dynamical system that couples mosquito populations with a human host population to study dengue transmission dynamics under the release of Wolbachia-infected mosquitoes. On this framework, we impose an optimal control problem aimed at minimizing a cost functional that balances biological and operational objectives: reducing dengue-infected humans, limiting the scale of mosquito releases, and incorporating baseline introduction costs. We further investigate the dynamics of varying Wolbachia strains to evaluate their potential for long-term population replacement and sustainable vector control.
Close AbstractBack to index
Undergraduate Session 5
WBC 403
2:15pm, Sean Funk (Millersville University)
Sean T Funk Real-Time Room Acoustics with Finite-Difference Methods and CUDA
View Abstract
Simulating sound in virtual environments—like VR or architectural walkthrough—requires fast and realistic modeling of how sound behaves in complex spaces. While geometric methods are fast, they cannot accurately capture the full impulse response of a room.
In this project, a higher-order finite-difference time-domain (FDTD) method is used to solve the 3D acoustic wave equation with the Robin boundary condition. The approximating method allows for a more accurate simulation of how sound waves move and reflect in space. To account for materials that absorb sound differently at different frequencies, an IIR filter is adopted to model frequency-dependent absorption. The simulation is implemented using Nvidia CUDA on GPUs rather than CPUs, which significantly improves computation time.
This approach can be used in architectural software for auralization and computing acoustical properties, and it can enhance virtual reality (VR) experiences through accurate room acoustics.
Close Abstract2:30pm, Kaden Hunter, Alexandra Ziegler, Peyton Haroldson (Millersville University of Pennsylvania)
Modeling Charged-Particle Motion in Electromagnetic Fields Using Differential Equations (Part I)
View Abstract
The motion of a charged particle in various electromagnetic field configurations is modeled using systems of ordinary differential equations. Beginning with the Lorentz force in a uniform magnetic field, the resulting linear system produces helical trajectories. The inclusion of a uniform electric field introduces a drift component to the motion. To account for energy dissipation, both linear and nonlinear damping terms are added, leading to nonlinear and nonautonomous systems. Linear damping yields gradual spiral decay toward equilibrium, while nonlinear damping results in more rapid stabilization. A time-varying electric field introduces frequency-dependent behavior and increased sensitivity to parameter values. Analytical methods and numerical simulations are employed to examine the dynamics of each system. These models offer insight into charged-particle behavior in physical settings such as plasma environments and auroral activity.
Close Abstract2:45pm, Kaden Hunter, Alexandra Ziegler, Peyton Haroldson (Millersville University of Pennsylvania)
Modeling Charged-Particle Motion in Electromagnetic Fields Using Differential Equations (Part II)
View Abstract
The motion of a charged particle in various electromagnetic field configurations is modeled using systems of ordinary differential equations. Beginning with the Lorentz force in a uniform magnetic field, the resulting linear system produces helical trajectories. The inclusion of a uniform electric field introduces a drift component to the motion. To account for energy dissipation, both linear and nonlinear damping terms are added, leading to nonlinear and nonautonomous systems. Linear damping yields gradual spiral decay toward equilibrium, while nonlinear damping results in more rapid stabilization. A time-varying electric field introduces frequency-dependent behavior and increased sensitivity to parameter values. Analytical methods and numerical simulations are employed to examine the dynamics of each system. These models offer insight into charged-particle behavior in physical settings such as plasma environments and auroral activity.
Close Abstract3:00pm, Nathan Tam (Penn State Berks)
Solving Nonlinear Second-Order “Doubly-Exact” Differential Equations
View Abstract
Traditional methods for obtaining analytical solutions for nonlinear second-order exact differential equations depend on the definition of an implicit solution 𝚿 as a function of x, y, and y’. This implicit solution is itself a first-order differential equation that may or may not be exact. This work defines a nonlinear second-order differential equation as “doubly exact” if the nonlinear second-order equation is exact and its implicit solution 𝚽, a function of x, y, and y’, is also exact, having an implicit solution 𝚿 as a function of x and y only. The additional condition of exactness at the first-order level allows the implicit solution 𝚿 to be derived exclusively from the nonlinear second-order equation.
Close AbstractBack to index
Undergraduate Session 6
WBC 404
2:15pm, Lukas Walko (Lebanon Valley College)
Entanglement Properties of Reduced NCP States
View Abstract
We study a class of quantum states called Werner states that have entanglement properties useful in theory and application. This talk concerns a specific subset of Werner states we call the NCP states. In particular, we explore the entanglement properties of the subsystems of NCP states. This investigation is motivated by the desire to prove the existence of a linear basis for Werner states with an appealing combinatorial description.
Close Abstract2:30pm, Mackenzie Carr (Lebanon Valley College)
Non-Crossing Polygons and Non-Crossing Chords
View Abstract
Motivated by a problem in quantum physics classifying a family of states called Werner States, we discovered that there exists a one-to-one correspondence between two special subsets of pure and mixed states. We construct states from diagrams called non-crossing chord (NCC) and non-crossing polygon diagrams (NCP). I will briefly explain how we get matrices and vectors from these diagrams. I will describe the functions that create the bijection between non-crossing chord diagrams and non-crossing polygon diagrams. I will also mention a connection to the Catalan numbers.
Close Abstract2:45pm, Daniel Cerra (The University of Scranton)
Lurching Forward with Historical Proofs
View Abstract
With the computer revolution, proof formalization has emerged as a new domain of research. In our research, we formalized a variety of historical proofs, including the proof of the irrationality of Euler's number $e$ and the proof for the sum of a geometric series using the proof assistant Lurch — new software designed to be accessible for undergraduate students. By formalizing Fourier’s original proof for the irrationality of $e$, we investigated the unstated assumptions and axioms that he was implicitly using at the time. This allows us to compare the historical version of a proof to a more rigorous formalized modern version.
Close AbstractBack to index