45th Annual WKU Mathematics Symposium Schedule and Abstracts
Schedule Overview
3:30pm (Friday)
Free registration is available throughout the whole event and begins at 3:30pm. It is located at Snell Hall First Floor. There will be free refreshments.
3:30 - 3:45pm
Dr. David Brown, Ogden College of Science and Engineering, Dean
3:45 - 4:45pm
Snell Hall 1108
5:00 - 6:25pm
Sessions will be in Snell Hall. For specific information see below.
6:30 - 7:00pm
Snell Hall First Floor near Da Vinci's.
7:00 - 8:25pm
Sessions will be in Snell Hall. For specific information see below.
8:30 - 9:15pm
Cody Lorton (Principal Scientist at Aviation and Missile Solutions), Evan Kessler (Actuary of the State of Indiana), Sarah Hartman (PhD Student at Middle Tennessee State University), Wilson Horner (Research Scientist at Riverside Research)
Snell Hall 1108
8:00 - 8:30am (Saturday)
Snell Hall First Floor
8:30 - 10:25am
Sessions will be in Snell Hall. For specific information see below.
10:45 - 11:45am
Snell Hall 1108
Detailed Schedule
Click on the Title and Presenter(s) to read the abstract of the presentation, and see a photo (when available).
Notes: (GA) Gatton Academy High School Student, (U) Undergraduate Student, (G) Graduate Student, (P) Postdoctoral Fellow, (F) Faculty, (I) Industry, * denotes presenter
Each 15-minute talk follows with a 5- to 10-minute Q&A. The next presenter should set up the presentation towards the end of the Q&A.
Friday, November 14
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Time |
Room |
Title and Presenter(s) |
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5:00-5:25pm
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SH 1101 |
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SH 1102 |
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SH 1103 |
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SH 1108 |
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5:30-5:55pm |
SH 1101 |
Multiplicities of Monomial Space Curves with Non-Noetherian Symbolic Blowups by Michael Reed* (F) |
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SH 1102 |
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SH 1103 |
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6:00-6:25pm |
SH 1101 |
Smith Normal Forms and Graphical Hermite Simplices by Antwon Park* (G) |
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SH 1102 |
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SH 1103 |
An Applied Mathematical Approach to Study Mathematical Structure: The Tornado Theory Cory Wang* (G) |
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7:00-7:25pm |
SH 1101 |
The Relationship Between M¨obius Transformations and the Poincare Metric Emma Bunch* (U) |
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SH 1102 |
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SH 1103 |
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7:30-7:55pm |
SH 1101 |
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SH 1102 |
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SH 1103 |
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8:00-8:25pm |
SH 1101 |
Floquet Theory for Differential Equations by Aryan Chinthala* (GA) |
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SH 1102 |
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SH 1103 |
Saturday, November 15
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Time |
Room |
Title and Presenter(s) |
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8:30-8:55am |
SH 1101 |
Filling chessboards to capacity with mutually non-attacking pieces Doug Chatham* (F) |
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SH 1102 |
Prediction of glioma tissue stiffness using metabolomic signatures by Vedant Garg* (GA) |
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SH 1103 |
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9:00-9:25am |
SH 1101 |
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SH 1102 |
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SH 1103 |
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9:30-9:55am |
SH 1101 |
From Fibers to Equations: A Guided Tour of Viscous Spinning Models Thomas Hagen* (F) |
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SH 1102 |
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SH 1103 |
Reforming Critical Thinking in Mathematics When Using AI by Ivan Lozano* (G) |
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10:00-10:25am |
SH 1101 |
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SH 1102 |
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SH 1103 |
Abstracts for Presentations
Title: Electroconvective Stability
Presenters: Fizay-Noah Lee* (F)
Abstract: We consider the Nernst-Planck-Navier-Stokes system, which is a PDE model that describes the electrodiffusion of charged particles (ions) in fluids. Such electrochemical systems are known to exhibit instabilities in both experimental and numerical settings. We investigate the stability properties of this system and explore what contributes (or does not contribute) to the onset of instability.
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Title: Multiplicities of Monomial Space Curves with Non-Noetherian Symbolic Blowups
Presenters: Michael Reed* (F)
Abstract: We present examples which extend those of Goto, Nishida, and Watanabe as well as introduce a new family of space monomial curves having small multiplicities which also have non-Noetherian symbolic blowups.
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Title: Smith Normal Forms and Graphical Hermite Simplices
Presenters: Antwon Park* (G)
Abstract: We will introduce the family of graphical Hermite simplices, which can be described as a slight perturbation of a diagonal n × n matrix with positive entries along the main diagonal, where the perturbation is being controlled by a simple directed acyclic graph on n vertices. We will share some results on sufficient conditions on the diagonal entries and the graph which yield a graphical Hermite simplex with a Smith Normal Form with a single nonunit invariant factor — i.e. having a cyclic cokernel — and on an upper bound on the invariant factors based on the lengths of paths in the directed graph.
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Title: The Relationship Between Möbius Transformations and the Poincar´e Metric
Presenters: Emma Bunch* (U)
Abstract: We present the relationship between Möbius transformations and hyperbolic geometry, a type of non-Euclidean geometry, in the upper half-plane using tools of complex analysis. We explore this relationship by first presenting the preliminaries of the stereographic projection and conformal mappings. We then present properties of Möbius transformations and formulas for the hyperbolic distance between two points. Specifically, we show hyperbolic distance is invariant under any Möbius transformation. Also, we use the Euler-Lagrange equation from the calculus of variations to prove that geodesics are either vertical lines or are parts of circles cen- tered on the x-axis. Lastly, we construct a specific mapping (Möbius transformation) and provide important results, which we use to prove the analog of Pythagoras’ Theorem in hyperbolic space.
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Title: Ideas Towards a New Geometry
Presenters: Chris Tiahrt* (F)
Abstract: In this presentation, I discuss a new set of axioms for geometry focused upon inclusion of all classical parallel postulates while retaining the Greek sensibility separating geometry from measurement. It admits a new class of interesting and meaningful finite geometries which will also be discussed.
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Title: Floquet Theory for Differential Equations
Presenters: Aryan Chinthala* (GA)
Abstract: This presentation is about the Floquet Theory, where we look at the matrix valued functions that satisfy Y ′(t) = A(t)Y (t) where A(t) is a periodic function and we find the structure of the solution Y (t). We also look at some properties of functions that satisfy the condition mentioned previously. After finding the form of our solutions, we can determine the stability of our function Y (t) in a simple way.
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Title: Filling chessboards to capacity with mutually non-attacking pieces
Presenters: Doug Chatham* (F)
Abstract: How many chess pieces can we place on the squares of an m × n chess board so that each piece attacks only empty squares? We discuss the process of finding this number (the “capacity” of the board) for given m and n, which turns out in most cases to be two-thirds m, rounded up, times n, plus 0, 1, or 2. We also discuss finding and counting the number of piece arrangements that have the maximum possible number of pieces, as well as variations on capacity, such as adding chess variant pieces, excluding pieces from the standard set, and using different kinds of boards.
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Title: Efficient Sampling in Constrained Domains: Skew-Reflected Non-Reversible Langevin Methods
Presenters: Hengrong Du * (F)
Abstract: Sampling efficiently from constrained probability distributions is crucial for many applications in Bayesian inference, statistical physics, and machine learning. We present a novel class of sampling algorithms based on Skew-Reflected Non-Reversible Langevin Dynamics (SRNLD). These dynamics incorporate skew reflection at the boundary to maintain constraint satisfaction and exploit non-reversibility to enhance convergence speed. We rigorously analyze the non-asymptotic convergence behavior of SRNLD in both total variation and 1-Wasserstein distances. Building on this, we propose a practical algorithm and prove its convergence to the desired distribution with bounded discretization error. Our methods outperform existing reversible algorithms in both theory and practice, as demonstrated by experiments on synthetic and real data.
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Title: From Fibers to Equations: A Guided Tour of Viscous Spinning Models
Presenters: Thomas Hagen* (F)
Abstract: The modeling of extrusion processes involving thin fluid threads and films with high viscosity leads to systems made up of transport equations coupled nonlinearly with the conservation of momentum equation in one or two spatial dimensions. Compared to the full quasi-static Stokes equations with free boundaries, these reduced models are significantly less complex and thus offer promising avenues for advancing the theoretical understanding of key manufacturing processes in polymer engineering. This presentation will provide a selective overview of the mathematical analysis of these governing equations, focusing on results concerning existence, stability, and long-time behavior of solutions.
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Title: Don’t Let the Pigeon in the Pigeonhole!
Presenters: Taylor Latham* (U)
Abstract: The Pigeonhole Principle is a fundamental tool in combinatorics. The Pigeonhole Principle will be discussed, proved, and applied.
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Title: Omnifinite Numbers and the Infinity Calculator
Presenters: Malleshwar Jayaraman Suresh, Anthony Lin, Elika Amin, Jake Cano Mauricio (GA)
Abstract: The Infinity Calculator is the world’s first fully defined arithmetic system capable of performing computations involving both finite and nonfinite numbers without producing mathematical errors. Built on the omnifinite number system, a closed extension of the reals and hyperreals, it introduces a complete arithmetic where all operations, including division by zero and indeterminate forms, yield valid numerical results. Within this framework, new special numbers such as absolute infinity and negative absolute infinity are defined as the largest positive and negative numbers in existence, creating a consistent structure where arithmetic is fully closed. The calculator follows standard PEMDAS order of operations, ensuring compatibility with classical computation. By eliminating undefined or indeterminate results, the Infinity Calculator offers a more robust mathematical model for advanced analysis, computation, and education. Its long-term goal is to extend into scientific and graphing errorless calculators, enabling more comprehensive studies in engineering, physics, and applied mathematics through a truly complete numerical system.
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Title: Data Science Added to WKU Math Masters and Undergraduate Programs (Plus a Graduate Certificate)
Presenters: Richard Schugart* (F)
Abstract: Pending final approvals, the Master of Science program in the Department of Mathematics will have a new Data Concentration starting in the Fall 2027. Additionally, we will offer a 12-credit Graduate Certificate in Statistical Data Science. The details of these programs will be presented. How these changes affect undergraduate program requirements will also be discussed. The remaining time will be used as a student Q&A.
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Title: Leveraging Machine Learning for Early Detection and Management of Hemoglobin A1c in Diabetic Patients
Presenters: Peter Agaba*
Abstract: There are more than 38.4 million people living with diabetes in the USA, which translates to 11.6% of the U.S. population. Diabetes is the eighth leading cause of death in the U.S. Effective management of Hemoglobin A1c (HbA1c) levels is crucial in reducing diabetes-related complications and improving patient outcomes. This paper explores the application of advanced machine learning (ML) and statistical techniques for the early detection and management of HbA1c levels in diabetic patients. Specifically, it classifies HbA1c levels of less than 8% as good control and levels greater than 9% as poor control. By classifying patients as high-risk versus non-risk using analytics, the paper recommends personalized treatment plans. This approach enhances glycemic control and advances precision medicine. The proposed system aims to offer diagnostic and treatment recommendations tailored to individual patients while implementing remote monitoring to reduce hospital readmissions and optimize healthcare resources. This works aims to transform diabetes care, improve patient outcomes, and reduce healthcare costs.
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Title: Mathematics of Communication Security: A Deep Dive into Frequency Hopping Spread Spectrum Signals and GPS Communication
Presenters: Wilson Horner*
Abstract: We live in a world with a constant flow of information, disguised as electromagnetic waves, propagating around the globe at near light speed. From mundane text messages to critical Positioning Navigation and Timing (PNT) data, different types of signals are in a constant fight to reach their respective destinations promptly and without losing data or being compromised. With our frequency bands becoming ever more congested and bad actors lurking about, how do we ensure that this information exchange has minimal latency and remains secure? How is everybody in the gym able to listen to their own music without eavesdropping on others? And how does your phone’s maps app know precisely where you are? We take a deep dive analyzing the math and science behind keeping our data safe, accurate, and fast while it navigates the complex electromagnetic spectrum.
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Title: Exponential Stabilization of Serially Connected Wave Equations: Continuous vs. Discontinuous Interface Control
Presenters: Zoe Brown* (G), Ahmet Ozkan Ozer (F)
Abstract: Systems governed by serially connected wave equations arise naturally in vibrating strings, flexible cables, electromagnetic transmission lines, and optical wave propagation. This presentation investigates the stabilization of two such wave equations equipped with an inertial tip that models a dynamic boundary element, such as a point mass or a reactive electrical load, under both continuous and discontinuous interface control designs. The configuration with continuous transmission conditions has been widely studied since the pioneering work of Hansen and Zuazua (SIAM J. Control Optim., 1995). The discontinuous design is inspired by the recent work of Ozer and Walterman (ECC, European Control Conference Proceedings, 2025), which addressed a related configuration without an inertial term, and is introduced here for the first time for this model. The proposed control law relies solely on velocity measurements of the left and right waves at the interface and achieves unconditional exponential energy decay without employing higher-order feedback-based damping or tip damping. Partial damping configurations leading to polynomial and conditional exponential stability regimes have recently been established for the continuous design in Akil, Brown, and Ozer (submitted, 2025). Different from that work, we develop a Lyapunov-based analysis establishing exponential stability for the discontinuous design and providing an explicit decay rate estimate. A structure-preserving Finite Difference approximation is constructed for both configurations to replicate the continuous energy balance and verify the discrete exponential decay. Numerical experiments confirm the theoretical predictions and demonstrate the superiority of the discontinuous interface approach. These novel results are part of an ongoing study currently under journal revision, reflecting the latest advances in the stabilization of serially connected wave systems.
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Title: Lyapunov-Based Exponential Stability Analysis of NASA’s SCOLE Model and SCOLE-inspired Beam-Mass-Beam Configuration with Rotational Inertia
Presenters: Kenedi Ashburn* (G), Ahmet Ozkan Ozer (F)
Abstract: We investigate the stability of two hybrid partial differential equation (PDE)-ordinary differential equation (ODE) models arising in engineering applications involving flexible structures and vibration control, such as spacecraft booms, robotic arms, and beam networks. The first model is NASA’s original SCOLE (Spacecraft Control Laboratory Experiment) configuration, first introduced in 1987, consisting of a cantilevered flexible beam carrying a tip mass at the free end. This model is not exponentially stabilizable with any lower-order feedback controllers. The higher-order boundary controllers employed here originate from the pioneering work of Rao (SIAM J. Control Optim., 1995), where uniform stabilization of hybrid elastic systems was first established. This model has been revisited recently by Akil, Ashburn, Brown, and Ozer (2025, preprint) for partial-damping configurations, where polynomial stability regimes were explicitly characterized and supported by novel Finite Difference approximations. The state of the art for the SCOLE model will be discussed, highlighting advances in stability characterization and numerical modeling. The novelty of the present work, to be presented in this talk, lies in developing a Lyapunov-based framework to establish exponential stability for the SCOLE model under the full-damping configuration. This approach provides explicit energy-decay estimates and is naturally compatible with Finite Difference approximations, offering a pathway toward continuous–discrete consistency and enabling the analysis of exponential and polynomial stability regimes for the approximated model in the full and partially damped cases. The second configuration considered is a SCOLE-inspired beam-mass-beam hybrid PDE-ODE system (proposed here for the first time), in which the inertial mass is positioned at an interior joint connecting two beams, and the rotational inertia of the interface is fully incorporated. Existing models in the literature have treated only simplified analogs of this configuration, primarily because the inclusion of the rotational-inertia term introduces substantial analytical challenges in the stability analysis. Analogous to the SCOLE setup, we design a feedback control law and apply, for the first time, a Lyapunov-based analytical framework to demonstrate exponential energy decay. This study complements recent works such as Akil, Ismail, Ozer, and Fragnelli (2025, submitted) and Akil, Ashburn, Brown, Fragnelli, Ismail, and Ozer (2025, submitted), which address interface (partial-damping) and tip-damping configurations, respectively. Unlike those resolvent-based analyses, the present work provides a constructive Lyapunov framework, yielding explicit energy estimates and a formulation more amenable to numerical and discrete stability studies. If time permits, we will also discuss Finite Difference approximations that preserve the identified stability regimes; however, the analysis of these discrete models is currently under investigation, and preliminary results will be shared with the audience.
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Title: Prediction of glioma tissue stiffness using metabolomic signatures
Presenters: Vedant Garg* (GA)
Abstract: Gliomas are aggressive tumors in critical need of improved therapeutic options. Recent work has demonstrated that glial tissue from core (inner) and edge (infiltrating) regions possesses distinct metabolic signatures and biomechanical properties that are linked to tumor aggression and migration. In this proof-of-concept study, Young’s moduli (stiffness) of core and edge tissue are predicted using paired metabolic signal intensities. Core and edge stiffness previously measured from n = 25 patients were paired with metabolomic data previously obtained using 2D liquid chromatography-mass spectrometry/mass spectrometry. Low (≤median) and high (>median) stiffness were predicted from paired core and edge metabolomics using a machine learning (ML) workflow that included forward feature selection, model training, grid search hyperparameter tuning, and repeated k-fold cross-validation. Key core metabolites predictive of low and high stiffness in core tissue included N6-methyllysine, 2’,3’-cyclic UMP, and gamma-amino-n-butyric acid. Top core metabolites in predicting edge moduli included guanosine, acetylcholine, glutamic acid, and N6-methyllysine. The top edge metabolite in predicting edge moduli was DL-p-hydroxyphenyllactic acid. Using ≤5 features, machine learning models predicted core and edge moduli using core and edge metabolites individually and in combination, achieving AUROC, maximum F1, and PRAUC values ≥0.90. This study shows that regions of differing glioma core and edge stiffnesses exhibit unique metabolic signatures. These signatures could potentially be explored to develop personalized therapeutic strategies.
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Title: Mathematical Modeling of Diabetic Foot Ulcers with Individual Patient Data
Presenters: Malleshwar Jayaraman Suresh*, Anthony Lin* (GA)
Abstract: A system of four ODEs has been developed within this research project to study the healing of diabetic foot ulcers by tracking the dynamics of MMP-1, TIMP-1, extracellular matrix (ECM), and fibroblasts. The model has previously been calibrated to averaged patient data, providing insight into the role of protease–inhibitor balance in tissue repair. We extend the model to individual patient data to capture variability and improve parameter estimation. A structural identifiability analysis is carried out on the full 12-parameter formulation to determine which parameters can be uniquely estimated with perfect data. The model is then fit to individual trajectories using nonlinear mixed-effects methods, producing both population-level and patient-specific parameter values. Parameter influence is being examined using Fisher Information Matrices and Spearman rank correlations. Insensitive parameters are fixed at nominal values, and the reduced model is re-fit. The resulting framework yields a biologically interpretable model with improved robustness for characterizing individual ulcer-healing dynamics.
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Title: Mathematical modeling of the behavioral response to mammalian grazing exposing insect herbivores to avian predation
Presenters: Sukurat Kofoworola* (G)
Abstract: This study formulates and analyzes mathematical models to investigate the behavioral and ecological impacts of mammalian grazing on grassland systems. Using systems of ordinary and partial differential equations, the research quantifies how grazing intensity modifies vegetation structure, insect herbivore exposure, and avian predation rates. Model parameters are estimated from experimental data, and the framework includes nondimensionalization for scalable analysis. The equilibrium and stability analyses are performed to characterize persistent change and identify crucial elements of population dynamics to explore the effects of grazing management strategies on trophic interactions. The study aims to provide predictive insights and a transparent modeling approach for optimizing diverse grassland ecosystems and supporting insectivorous bird populations.
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Title: The Black-Scholes PDE Framework: An Investigation into the Application of Geometric Brownian Motion for European Option Valuation
Presenters: Arion Ford* (U)
Abstract: This project establishes the framework for valuing European options, assuming the underlying asset follows a Stochastic Differential Equation known as Geometric Brownian Motion (GBM). By employing Itˆo’s Lemma and the Delta Hedging argument, we construct a risk-free portfolio that eliminates all stochastic terms, effectively simplifying the system to a deterministic state. Using the No-Arbitrage Principle, we transform this system into the foundational Black-Scholes Partial Differential Equation (PDE). The analysis culminates in a change of variables that reduces the PDE to the classical Heat Equation, leading to the well-known closed-form pricing formula. This process demonstrates that robust mathematics can provide analytical solutions for complex financial randomness.
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Title: Summary of a Summer Summing Some Sums
Presenters: Dominic Lanphier* (F)
Abstract: There are many ways to show that an infinite sum sums to a number. There are far fewer ways to actually sum the sum. For example, we learned about geometric series, and Leibniz summed some interesting sums using calculus. The first real exciting sum was the Basel problem, first solved by Euler. Nowadays there are many ways to solve the Basel problem, and a classical method to solve it uses complex analysis. Last summer, we used complex analysis to find a new way to sum some infinite sums. We use this to give new ways to sum old sums, such as the Basel problem, and we sum some new infinite sums.
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Title: Computational Approaches to Partitioned Versions of the Erdos–Szekeres Theorem Using Linear Optimization
Presenters: Andrew Oluwashijibomi Adegoju *(G), Attila Por (F)
Abstract: This work is related to the partitioned versions of the Same type lemma and the Erdos-Szekeres theorem, which states that for every integer kgeq3, there exists a minimum number ES(k) such that any set of at least ES(k) points in the plane in general position contains k points forming a convex polygon. The partitioned colorful version of the Same type lemma states that given n sets in the d-dimensional space of equal size, one can partition each set into c(n,d) parts such that for each part each transversal has the same type, and each part has the same size. The research focuses on a computational approach of a partitioned versions of the Same type lemma in one dimension, focusing on constructing and verifying balanced, separable partitions for point sets using linear optimization techniques. It formulates the problem as a linear system representing geometric, balanced, separable and partition constraints, and employs linear programming approach to algorithmically construct and verify the existence of partitions that satisfy balanced and separability criteria. This work was motivated by open problems on the existence and bounds of convex transversals in partitioned sets. The work aims to improve the known bounds for n3,1 (3 distinct point sets in 1 dimensional), using computational linear programming to validate and extend classical combinatorial geometry results. This approach establishes a novel computational framework that bridges combinatorics, discrete geometry and optimization.
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Title: An Applied Mathematical Approach to Study Mathematical Structure: The Tornado Theory
Presenters: Cory Wang* (G)
Abstract: Mathematical structure refers to the characteristics, topology, dynamics, and relationships within and between mathematical concepts invariant to the contexts and interpretations which instantiate the concepts. According to the structuralist philosophy of mathematics, structure is the fundamental building block of mathematics, but the notion of mathematical structure also plays a key role in other realist philosophies of mathematics such as Platonism and Lakoff and Núñez’s embodied cognition (2000). I will propose and explicate an emergent theoretical framework, the Tornado Theory, which emerges from the structuralist, Platonist, and embodied cognitive views to characterize the mathematical structure. In particular, the Tornado Theory proposes a duality between the Platonist and embodied cognitive approaches, which when mediated by mathematical structure, is “the driving force behind the incessant growth of [mathematical] knowledge” (Sfard, 2003, p. 359). I suggest the Tornado Theory, when synthesized with approaches from applied mathematics, such as network theory, information theory, and dynamical systems theory, could reveal key structural information about the discovery, creation, teaching, and learning of mathematics.
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Title: Hybrid transformer–LSTM with multitask quantile learning for Bitcoin volatility and value-at-risk (VaR) forecasting
Presenters: Emmanuel Tomiwa Siyanbola* (G)
Abstract: Cryptocurrency markets such as Bitcoin are well known for their extreme ups and downs, which makes managing financial risk especially challenging. Traditional models, while useful, often struggle to capture the complex patterns in these markets. This study develops a hybrid deep learning model that combines two powerful approaches—Transformers (which are effective at capturing long-term patterns) and Long Short-Term Memory (LSTM) networks (which specialize in short-term dynamics). The model employs a multitask learning strategy to forecast both volatility and Value-at-Risk (VaR), a common measure of extreme losses. The study covers daily Bitcoin data from 2010 to 2025, along with relevant financial indicators such as the VIX (fear index), Fear & Greed Index, and on-chain metrics describing blockchain fundamentals. The model is trained on historical data and evaluated against several benchmarks: Historical Simulation, GARCH (a widely used econometric model), a standalone LSTM, and a standalone Transformer. Performance is assessed using both accuracy (mean squared error and mean absolute error) and risk reliability (statistical backtests of VaR). Our findings show that the hybrid model provides more reliable and well-calibrated risk forecasts than either traditional econometric models or single-model deep learning approaches. This work demonstrates the potential of modern machine learning in financial risk management and highlights how combining specialized architectures can improve decision-making in volatile markets like cryptocurrencies.
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Title: A New Class of Probability Distributions via Half-Elliptical Functions
Presenters: Lukun Zheng* (F), Ngoc Nguyen* (F)
Abstract: We develop a new family of distributions supported on a bounded interval with a probability density function that is constructed from two elliptical arcs. The distribution can take on a variety of shapes and has three basic parameters: minimum, maximum, and mode. Compared to classical bounded distributions such as the beta and triangular distributions, the proposed semi-elliptical family offers greater flexibility in capturing diverse shapes of distributions, in symmetric and asymmetric settings. Its construction from elliptical arcs enables smoother transitions and more natural tail behaviors, making it suitable for applications where classical models may exhibit rigidity or over-simplicity. We give general expression for the density and distribution function of the new distribution. Properties of this distribution are studied and parameter estimation is discussed. Monte Carlo simulation results show the performance of our estimators under many sets of situations. Furthermore, we show the advantages of our distribution over the commonly used triangular distribution in approximating beta distributions
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Title: Analyzing a Structurally Identifiable Model for Tuberculosis Transmission Using Data from Bangladesh
Presenters: Anika Tahsin* (F)
Abstract: Tuberculosis (TB) remains a major public health challenge in Bangladesh, intensified by increasing multidrug-resistant (MDR) cases. We developed a compartmental differential-equation model that describes the transmission dynamics of drug-sensitive and MDR-TB and incorporates infection, progression, treatment, recovery, and reinfection. The model’s stability was analyzed using the basic reproduction number, and the full system was shown to be structurally identifiable. To apply the model to data, the system was reduced to six differential equations and curve fitted to TB case data from Bangladesh (2010–2019). Practical identifiability of key parameters was evaluated using the Fisher Information Matrix and a modified profile likelihood approach. The reduced model fit the data well, and several epidemiologically relevant parameters were found to be practically identifiable, while others remained weakly identifiable, emphasizing the need for richer surveillance data. Overall, the model provides a rigorous framework for understanding TB transmission and supports data-driven decision making in high-burden settings.
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Title: Promoting a Critical Stance in an Inquiry-Oriented Dynamical Systems and Modeling Course
Presenters: Melanie Stewart* (UG/G), Nicholas Fortune* (F)
Abstract: We will present the design of Inquiry-Oriented Dynamical Systems and Modelling (IODSM), an upper-division mathematics content course that can serve as an elective for prospective secondary teachers (PSTs). The course bridges university and secondary mathematics by combining advanced content with structured opportunities to engage secondary mathematics topics, forward-looking teaching practices, and the Standards for Mathematical Practice. Grounded in Inquiry-Based Mathematics Education and oriented toward fostering productive dispositions such as students’ embracement of a critical stance, IODSM offers a learning environment where PSTs connect mathematics with future teaching. In this presentation we outline a typical class day, describe our theoretical grounding, and highlight four design principles that guide the design of classroom activities, student materials, and instructional choices. We conclude with evidence of PSTs’ willingness to critically reflect on their mathematical beliefs and values, resulting in students embracing a critical stance.
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Title: Connecting Real Analysis to High School Mathematics
Presenters: Sarah Hartman* (G), Zachary Bettersworth* (F), Nick Fortune* (F)
Abstract: Upper-division mathematics courses, such as Real Analysis, can provide in-service teachers with opportunities to make connections between their understanding of real analysis content and teaching high school mathematics. Recent research has sought to deepen this connection for pre-service teachers. However, our context is different, that is, we offer an online real analysis graduate course for in-service high school teachers. We detail how this course was designed and the research conducted to understand the connections that in-service teachers make between their learning of real analysis and their teaching of high school mathematics.
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Title: Reforming Critical Thinking in Mathematics When Using AI
Presenters: Ivan Lozano* (G)
Abstract: Artificial intelligence (AI) presents transformative possibilities for mathematics education by reshaping how students engage with mathematical concepts. This presentation introduces a proof-of-concept study exploring an AI-mediated instructional method where students iteratively refine mathematical definitions through dialogue with large language models (LLMs). Grounded in research linking definition generation with deeper understanding (de Villiers, 1998; Edwards & Ward, 2004), the study investigates how structured feedback from LLMs may support conceptual development before large-scale classroom implementation. Two research questions guided the investigation: (1) Which features of simulated LLM conversations are associated with improved definitions? and (2) How does question type relate to improvement likelihood? The authors simulated 646 refinement interactions across three LLMs (ChatGPT, Copilot, and Gemini) using two mathematical objects (ray and quadrilateral), varying initial definitions and feedback strategies (agreement or questioning). Logistic regression analysis (McFadden R = 0.301) revealed significant interactions between object, language model, and feedback type. Students were more likely to improve definitions of rays than quadrilaterals, suggesting mathematical complexity affects learning potential. Early refinements showed the highest improvement odds, indicating diminishing returns with repetition. Funneling questions produced over twelve times greater improvement odds than focusing questions, though their cognitive depth remains uncertain. For improvement of definitions, ChatGPT outperformed Gemini, with Copilot yielding intermediate results, all of which underscored model-specific differences. This proof-of-concept demonstrates the potential of LLMs to scaffold definition-making while fostering students’ critical engagement with AI-generated feedback; pushing back against the banking model of knowledge LLMs seemingly enforce (Freire, 2000). Future research will refine this method before classroom implementation to develop students’ independent, reflective reasoning.
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Title: Fostering Preservice Elementary Teachers’ Conceptual Understanding and Mathematical Reasoning through Problem Posing
Presenters: Sarvani Pemmaraju* (G)
Abstract: I will share a task designed for elementary preservice teachers in an introductory mathematics content course that prompted them to create a fraction multiplication problem. The task engaged preservice teachers in generating word problems on fraction multiplication, modelling them to develop a deeper understanding of the concept and connecting these models to the traditional algorithm they learned in school. The goal of this lesson was to help preservice teachers explore different ways to multiply fractions, recognize the connections between these varied ways and represent them visually in multiple ways so that they have a variety of tools to answer their students’ “why” questions. In this context, I will describe preservice teachers’ conceptions along with patterns in their thinking, as well as major hurdles observed in their understandings.
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Title: Neural Dynamic Time Warping: A Differentiable Framework for Financial Bubble Analysis
Presenters: Lukun Zheng* (F)
Abstract: This research presents Neural Dynamic Time Warping (Neural-DTW), a novel framework that learns optimal time warping functions for financial bubble analysis. By replacing traditional dynamic programming with a monotonic attention mechanism, our approach learns to align time series while incorporating multi-dimensional market features. In our exploratory analysis comparing dot-com and AI bubbles, Neural-DTW shows promising potential for reducing alignment error and producing more economically plausible temporal mappings compared to classical methods. This work formalizes time warping as a learnable optimization problem, bridging neural networks with time series analysis for improved financial pattern recognition.
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