Session Index
Click a session title to jump to the abstracts.
Undergraduate Session 1
2:15pm--3:15pm, Woodland 121
Speakers: Paige Foley, Jaire Bartlett, Auris Espinal, Anna Nguyen, Alexa Rogers, Ellery Panaia, Maggie Pulliam
Undergraduate Session 2
2:15pm--3:15pm, Woodland 124
Speakers: Mady Hubbard and Tamia Lewis, Abigail Thomas, Diya Sara Mathew, Samuel Nguyen, Daniel Magosin, Alec Posner, Jane Meade
Undergraduate Session 3
2:15pm--3:15pm, Woodland 220
Speakers: Jo Amuso, Sean Kljuco, Kelsey Nager
Undergraduate Session 4
2:15pm--3:15pm, Woodland 313
Speakers: Nicolas Hipolito, Tommy Pham, Sophie Nasir, August Butcher, Liz Callan, Andrew Lopez
Undergraduate Session 5
2:15pm--3:15pm, Woodland 319
Speakers: Anastasia Clements, Alexander Nappo, Jay Patwardhan, Jon R. Cohen
Undergraduate Session 1
Woodland 121
2:15pm, Paige Foley (Saint Joseph's University)
The Contributions of Edward Tufte to Data Visualization
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In today’s data-driven world, the ability to communicate complex information with clarity and precision is crucial. In this presentation, we will talk about the life of Edward Tufte, his contribution to the field of data visualization and design along with the visual presentation of complex material. We will analyze how Edward Tufte’s principles play a role in how we present information in today’s data-driven world.
Close Abstract2:30pm, Jaire Bartlett, Auris Espinal (Saint Joseph's University)
The Legacy of Alan Turing
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Various mathematicians have made many contributions to our society. One of the brightest among them is Alan Turing. Commonly acknowledged as the father of computer science, he established the foundation of theoretical computer science. This presentation aims to highlight Turing’s impact on the world of mathematics. It will give a summary of Turing’s early life but explicitly focus on the impacts and the consequences of his innovations during his time and up to ours.
Close Abstract2:45pm, Anna Nguyen, Alexa Rogers (Saint Joseph's University)
Hypatia of Alexandria
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Our talk will be about the Greek mathematician, Hypatia of Alexandria. She is most notable for being the earliest known female mathematician. Regarded highly for her skills at both mathematics and public speaking, she went on to accomplish remarkable things, such as devising a new, easier method of long division for astronomers to improve on Ptolemy’s old method. Sadly, she was murdered by a Christian mob for being a pagan. Today, she is a symbol of empowerment for women in math and science.
Close Abstract3:00pm, Ellery Panaia, Maggie Pulliam (Saint Joeseph's University)
Michel Rolle's Legacy
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Michel Rolle was a self-taught mathematician whose influence on the history of mathematics cannot be understated. In this presentation, Michel Rolle’s life, mathematical works, and their significance in today's world will be explored and expanded upon to uncover the great legacy of Michel Rolle.
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Undergraduate Session 2
Woodland 124
2:15pm, Mady Hubbard and Tamia Lewis (Saint Joseph’s University)
The Life of Katherine Johnson
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Katherine Johnson was a mathematician from America who played a large part in the success of early space missions put on by NASA. Throughout her career, Johnson broke many barriers as an African American woman in a male-dominated field, gaining recognition for her precision and dedication. During this presentation, we will discuss Katherine Johnson's many accomplishments, the obstacles she faced, and the impact she has left on mathematics.
Close Abstract2:30pm, Abigail Thomas, Diya Sara Mathew (Saint Joseph’s University)
Life and Contributions of Srinivasa Ramanujan
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Srinivasan Ramanujan is an Indian mathematician who contributed significantly in the mathematical domain during the twentieth century. He had no traditional degree or education but significantly contributed to mathematics. His contributions to mathematics include mathematical analysis, infinite series, continued fractions, number theory, and more.
Close Abstract2:45pm, Samuel Nguyen, Daniel Magosin (Saint Joseph's University)
The History of Fermat's Last Theorem
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Fermat’s Last Theorem states that no three positive integers, such as a, b, and c, satisfy the equation of a^n+b^n = c^n, where n is any integer value greater than n = 2. This theorem, proposed by Pierre de Fermat, a 17th-century mathematician, has puzzled mathematicians for centuries. This presentation will discuss the origin of Fermat’s Last Theorem, using numerical examples and applied contexts in the mathematical world, as well as the attempts to solve and disprove the theorem.
Close Abstract3:00pm, Alec Posner, Jane Meade (Saint Joseph’s University)
The Banach-Tarski Paradox
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In this presentation, we will explore the mathematical underpinnings of the Banach-Tarski Paradox, including group theory and measure theory, and discuss the implications of such decompositions in understanding the nature of infinity. We will also address the limitations of this result in practical contexts, emphasizing that such constructions are purely theoretical and cannot occur in physical reality. Through this exploration, we aim to illustrate how the Banach-Tarski Paradox broadens perspectives on mathematical infinity and challenges our assumptions about continuity and volume in mathematics.
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Undergraduate Session 3
Woodland 220
2:15pm, Jo Amuso (Bryn Mawr College)
Using Biomathematical Models to Examine Potential Effects of Semaglutide on Polycystic Ovarian Syndrome Treatment
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Semaglutide, better known by its brand name Ozempic, is a drug used to treat Type 2 diabetes. It activates the GLP-1 receptor, which is vital for the regulation of insulin and glucose levels in the bloodstream. Ozempic has also shown promise as a treatment for polycystic ovarian syndrome (PCOS), a hormone imbalance in people with uteruses often characterized by an abnormal menstrual cycle and insulin resistance. However, the mechanisms behind PCOS are not clearly understood, and the reasons behind the effectiveness of Ozempic as a PCOS treatment remain unclear. Since GLP-1 receptors belong to a class of receptors called G protein-coupled receptors, we can form hypotheses about the relationship between Ozempic and PCOS by adapting general mathematical models of G protein-coupled receptors to fit the specifications of GLP-1 receptors. We can then analyze these new models in conjunction with models of reproductive hormone levels, insulin levels, and semaglutide levels in the bloodstream.
Close Abstract2:45pm, Sean Kljuco (Saint Joseph's University)
Math in Medicine
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Although many are aware of the importance of certain disciplines like statistics in medicine and science, many are unaware of how important other aspects of math are in medicine. Whether through formulas that use simple variables like body weight and surface area affected to more complex formulas and concepts that allow for the use of modern technology like CT scans math has a much greater presence in most aspects of medicine. This presentation seeks to highlight some of the lesser-known uses of mathematics in medicine, focusing on specific examples within medicine to show how vital math is to modern medicine and saving lives.
Close Abstract3:00pm, Kelsey Nager (Saint Joseph's University)
Leveraging ChatGPT to Revolutionize Probability and Statistics Education
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Generative AI, such as ChatGPT, has the potential to revolutionize probability and statistics education. This talk will briefly review what Large Language Models are and how they process and learn information. I will summarize the most recent findings on AI models, specifically ChatGPT's ability to teach statistics concepts. Then, I will guide the audience through an exploration of ChatGPT’s responses to various questions in probability and statistics to illustrate its current capabilities. The talk concludes with a summary of the limitations and opportunities for ChatGPT and other Large Language Models in helping students learn probability and statistics.
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Undergraduate Session 4
Woodland 313
2:15pm, Nicolas Hipolito (University of Scranton)
A Crash Course in Quantum Tic-Tac-Toe
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Assuming minimal background in mathematics and physics, we will demonstrate core concepts of quantum mechanics. Through Quantum Tic-Tac-Toe, we look at superposition, entanglement, and measurement. By the end, we will have shared an engaging game which can demonstrate these concepts for all ages.
Close Abstract2:30pm, Tommy Pham (Temple University )
Investigating Lucas Sequences Under A Modulus
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In this research, we will investigate various Lucas sequences under a modulus. These are known to be
periodic. One of the key objectives is to calculate all moduli that yield a given period. While there exist methods and algorithms for computing moduli (m) such that π(m) = k, denoting a period, the existing theorems are specific to the Fibonacci sequence. Our aim is to generalize and strengthen these theorems while ensuring consistent results.
Close Abstract2:45pm, Sophie Nasir, August Butcher (Gettysburg College)
Romantic Love in the Brain and Simple Addiction Models
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"Love is an addiction," as songwriter Richie Campbell states, might be a more accurate declaration than one might think. There are stark similarities between behaviors associated with early-stage romantic love and addiction: sleeplessness, hyperactivity, increased concentration, and dependency, among others. The main neurotransmitter responsible for much of the overlap is dopamine, which we focus on in this talk. Our team investigated how well addiction models of dopamine production translate to the context of early-stage romantic love. We will present two linear differential equations from the addiction literature and our resulting analysis to show how they capture macro-level dopamine production but fall short on smaller timescales.
Close Abstract3:00pm, Liz Callan, Andrew Lopez (Gettysburg College)
Computational Models for Addiction and Model Building in the Context of Romantic Love
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This talk explores the biochemistry of the brain during early-stage romantic love beyond the main variable of dopamine. We present a fuller system by incorporating the influence of the neuropeptide orexin on dopamine production. Since simple linear differential equations are inadequate for modeling the brain in this regime, we turn to neuroscience learning models and nonlinear ordinary differential equations. Building on the literature, our team arrives at a system of ordinary differential equations that integrate behavioral and computational approaches which can capture dynamics on multiple time scales. Each refinement in the process offers a deeper understanding of the neurochemical processes involved while attempting to balance fine detail and the big picture. Through this approach, we aim to shed light on the complex interplay between emotion, behavior, and biology in intense romantic attachment.
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Undergraduate Session 5
Woodland 319
2:15pm, Anastasia Clements (West Chester University)
Proportionally Geometric Cantor Set
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Cantor sets are mathematical objects whose geometric and analytic properties may vary with the construction used to define them. Notably, the usual middle-third Cantor set has a measure of 0 and a property of self-similarity. Another well-studied variation of the Cantor set is the Smith-Volterra-Cantor set, which has positive measure but loses its self-similarity.
In this talk, I'll introduce both of these versions of the Cantor set, discuss their properties, and we'll explore a variation of the Cantor set which has positive measure and retains a property of proportionality.
Close Abstract2:30pm, Alexander Nappo (Villanova University)
On intersecting families of independent sets in paths and path-like graphs
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The Erdos-Ko-Rado (EKR) theorem, a foundational result in extremal finite set theory, states that any family of k-subsets of a finite set containing at least 2k elements that is intersecting, i.e. the family has the property that no two subsets in it are disjoint, can be no bigger than the family of all k-subsets containing a fixed element x. The latter family is trivially intersecting and is called a star centered at x. We discuss recent work on a graph-theoretic generalization of the theorem, focusing in particular on the path and the pendant path graphs. We consider the auxiliary problem of ordering the sizes of stars in these graphs and offer additional insight into the structure of non-star intersecting families.
Close Abstract2:45pm, Jay Patwardhan (Rutgers University New Brunswick)
Generalized Mazur Patterns and Immersed Heegaard Floer Homology
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Generalizing prior work of Levine, we give infinitely many examples of pattern knots P such that P(K) is not slice in any rational homology 4-ball, for any companion knot K. To show this, we establish a closed formula for the concordance invariants tau and epsilon of a family of satellite knots obtained from generalized Mazur patterns. Our main computational tool is the immersed curve technique from bordered Heegaard Floer homology arising from the work of Chen-Hanselman.
Close Abstract3:00pm, Jon R. Cohen (Muhlenberg College)
Adventures in Single Elliptic Geometry
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The unmarked straightedge and compass are the two fundamental tools for any geometer. With twenty-three definitions and ten axioms, including the infamous parallel postulate, Euclid of Alexandria (circa 300 BCE) developed Euclidean Geometry. In the 19th century, geometers began to explore non-Euclidean geometries, where the parallel postulate is swapped for another axiom. In Single Elliptic Geometry, the model of which is the Klein Disk, any two lines intersect in exactly one point. We build on previous work that describes the construction of a Single Elliptic straightedge and compass. We also demonstrate that while the first four postulates of Euclid hold in this model, not all of the propositions from Neutral Geometry are valid. This points out the incompleteness of Euclid’s axioms.
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