Time Zone Notice. All official talk times below are listed in US Central Time (America/Chicago). Use the local-time link beneath a talk or session block to convert it to your own time zone. On August 8–9, 2026, America/Chicago observes Central Daylight Time (CDT, UTC−5).
Session Time Blocks
Program Schedule
- Talk 01 — Sayandip Pandit (Department of Mathematics, IIT Delhi, India) — August 8, 2026 | 8:30 AM–9:00 AM (US Central Time)Title: Geometric Puzzles on a Circular Track: A Recreational Introduction to Quantization
Abstract
Imagine a circular running track with several water stations placed around it. If only a few stations may remain open, or if a few new stations may be built, where should they be located so that runners travel the shortest possible distance to reach one? This simple question leads to a collection of recreational geometry puzzles involving distance, symmetry, optimization, Voronoi regions, and quantization. Quantization is the mathematical problem of replacing a large collection of points by a smaller set of representative points while minimizing the approximation error. Using only elementary mathematics, we investigate several configurations of points on a circle and discover elegant optimal arrangements. The article illustrates how sophisticated mathematical ideas can arise naturally from simple geometric games and puzzles, providing an accessible introduction to concepts that play important roles in geometry, optimization, data science, signal processing, and approximation theory.
▶ Video 📄 Slides - Talk 02 — Richa Jain (Visvesvaraya National Institute of Technology, Nagpur, Maharashtra, India) — August 8, 2026 | 9:00 AM–9:30 AM (US Central Time)Title: Constrained Rational Spline and its Applications in Solving Differential Equations
Abstract
In this talk, we explore the constrained univariate and bivariate rational splines. We begin by constructing a univariate rational spline that either lies above or below the specified piecewise line or is contained within a specified rectangle. Subsequently, we construct a bivariate rational spline using the blending technique. Sufficient conditions are identified so that the proposed bivariate rational spline lies above or below the specified plane or remains within a given cuboid. The proposed constrained splines are utilised to solve constraint differential equations. Numerical examples are provided to verify the proposed theoretical results.
▶ Video 📄 Slides - Talk 03 — Pavjeet Singh (Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, India) — August 8, 2026 | 9:30 AM–10:00 AM (US Central Time)Title: Constrained Quantization for Uniform Distributions with Two Constraint Families
Abstract
This paper investigates constrained quantization for a uniform probability distribution supported on the unit interval, with respect to two distinct families of geometric constraints. For the first family consisting of straight-line segments parallel to $y = x$, we explicitly determine the constrained optimal sets of $n$-points for all $n \in \mathbb{N}$ and compute the corresponding constrained quantization errors. We further establish the existence of the associated constrained quantization dimension, showing that it equals two, and evaluate the corresponding quantization coefficient. For the second family, composed of concentric circles, we develop a systematic methodology to obtain constrained optimal sets of $n$-points together with their constrained quantization errors. Several illustrative examples are provided to demonstrate the computational procedure. The results reveal structural phenomena unique to constrained quantization, including optimal sets with fewer than $n$ points and quantization dimensions that need not coincide with the Euclidean dimension of the underlying support. These findings underscore the complexity of quantization under geometric restrictions and open avenues for further theoretical and computational developments.
▶ Video 📄 Slides - Talk 04 — Prabhat Tamrakar (Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, India) — August 8, 2026 | 10:00 AM–10:30 AM (US Central Time)Title: Geodesic quantization, optimal sets of $n$-means, probability measures on the sphere, spherical isometries, spherical distributions, Voronoi decomposition
Abstract
Geodesic quantization of probability measures on the unit sphere S2 with its intrinsic geodesic metric is studied. We are interested in the geodesic distortion functional and the n−th quantization error for a Borel probability measure on S2. With the help of the compactness of the sphere and the continuity of the distortion functional, we prove that the optimal sets of n−means exist. We show that the distortion functional is invariant under spherical isometries and we obtain symmetry principles for probability measures invariant under groups of isometries. We also get a Voronoi decomposition of the distortion functional by assigning points of the sphere to the nearest quantizer points and performing the tie-breaking procedure in order to obtain a true Voronoi partition. We obtain the quantization representation of the distortion functional for finite-support probability measures and demonstrate that the quantization error is equal to zero if the number of quantizer points is not less than the number of support points. This coherent treatment gives an idea of future explicit computations of optimal quantizers and optimal quantization errors for highly symmetric spherical configuration.
▶ Video 📄 Slides - Talk 05 — Hui-Yi Hsu (University of Wisconsin-Milwaukee, USA) — August 8, 2026 | 10:30 AM–11:00 AM (US Central Time)Title: Reflection Coupling and Quantitative Convergence to Equilibrium for Diffusion Processes
Abstract
This talk presents the main idea of Theorem 2.1 in Quantitative Harris-Type Theorems for Diffusions and McKean–Vlasov Processes by Andreas Eberle, Arnaud Guillin, and Raphael Zimmer. The authors study diffusion processes with additive noise under a generalized one-sided Lipschitz condition on the drift and a geometric Lyapunov condition. Their goal is to obtain quantitative estimates for the long-time behavior of these processes. The main idea is to combine reflection coupling with a concave distance function and a Lyapunov function. Reflection coupling controls the distance between two copies of the diffusion, while the Lyapunov function provides global control when the processes move far from the origin. By combining these two mechanisms, the authors construct a suitable Kantorovich distance and establish exponential contraction with an explicit contraction rate. Finally, I will discuss a direction for future research involving regime-switching diffusion processes, which provide a versatile and realistic framework for a wide range of applications. Despite their importance, their long-term behavior, particularly ergodicity and large deviation principles, remains relatively underexplored. Motivated by the coupling method developed in this paper, we aim to extend this approach to study the ergodicity of regime-switching processes and explore its potential applications to stochastic ergodic control and game problems.
▶ Video 📄 Slides - Talk 06 — Bismark Bimpong (The University of Texas Rio Grande Valley, USA) — August 8, 2026 | 11:00 AM–11:30 AM (US Central Time)Title: Constrained Quantization
Abstract
This talk provides an accessible introduction to constrained quantization, a mathematical framework for approximating large collections of data by a smaller set of representative points while satisfying prescribed geometric constraints. Beginning with the familiar idea of rounding, the presentation explains how quantization selects representative points (a codebook) to minimize the average squared approximation error. It then contrasts unconstrained quantization, where representatives may be placed freely, with constrained quantization, where they must lie on an allowed set such as a line, curve, or boundary. Through intuitive examples, Voronoi regions, and simple geometric illustrations, the audience will see how constraints fundamentally change the optimal representatives and the resulting approximation error. The talk concludes by highlighting applications in data compression, clustering, signal processing, optimization, and geometry, while providing a glimpse into current research on constrained quantization for discrete probability distributions under geometric constraints. Designed for undergraduate students, the presentation requires only basic ideas of distance and averages, making advanced concepts accessible without assuming prior knowledge of probability theory or measure theor
▶ Video 📄 Slides - Talk 07 — Matheus Mauricio Santos Gomes (University of Central Florida, USA) — August 9, 2026 | 8:30 AM–8:45 AM (US Central Time)Title: UFC Winner Prediction using Machine Learning
Abstract
Title: UFC Fight Outcome Prediction Using Fighter Performance Metrics and Machine Learning Abstract: This project, conducted by **Matheus Gomes** and **Joaquin Hidalgo-Estrada**, explores the use of machine learning techniques to predict the outcomes of Ultimate Fighting Championship (UFC) fights using fighter performance metrics rather than fighter identities. Mixed martial arts presents a unique predictive challenge due to the combination of striking, grappling, physical attributes, and fighter experience that influence fight outcomes. To address this problem, historical UFC fight data obtained from UFCStats and Kaggle datasets are being analyzed to identify patterns associated with winning performances. The project focuses on developing predictive models using fighter statistics such as striking efficiency, takedown effectiveness, submission activity, physical characteristics, and career performance indicators. Several machine learning algorithms, including Support Vector Machines (SVM), Random Forests, and Extreme Gradient Boosting (XGBoost), are being evaluated and compared. Feature engineering techniques are used to create matchup-based variables that quantify differences between fighters, such as reach, age, striking metrics, and grappling performance. In addition, the project investigates the development of a fighter rating system that summarizes overall fighter quality into a single performance score for use in predictive modeling. Through this work, we aim to identify the fighter characteristics that contribute most to success in the UFC and assess the effectiveness of machine learning for sports analytics applications. By focusing on performance-based statistics rather than fighter names, the proposed framework seeks to improve model generalizability, interpretability, and predictive accuracy while providing meaningful insights into competitive mixed martial arts.
▶ Video 📄 Slides - Talk 08 — Joaquin Hidalgo-Estrada (University of Central Florida, USA) — August 9, 2026 | 8:45 AM–9:00 AM (US Central Time)Title: UFC Winner Prediction using Machine Learning
Abstract
This project uses machine learning to predict UFC fight winners based on historical fighter statistics, physical attributes, and performance data available before each fight. Different classification models are compared to identify the most effective approach, while addressing challenges such as target leakage and feature selection. The results demonstrate the potential of data science techniques in sports outcome prediction. I will be speaking alongside project collaborator Matheus Santos Gomes who also submitted a form.
▶ Video 📄 Slides - Talk 09 — Bernardo Benitez (The University of Texas Rio Grande Valley, USA) — August 9, 2026 | 9:00 AM–9:15 AM (US Central Time)Title: Magic Squares: Patterns, Puzzles, and Mathematical Thinking
Abstract
A magic square is a square arrangement of numbers in which the sum of the numbers in every row, every column, and the two main diagonals is the same. Although magic squares appear simple, they contain rich mathematical ideas involving patterns, arithmetic, symmetry, logical reasoning, and problem-solving. In this interactive workshop, school students will explore a three-by-three magic square, discover its magic sum, complete missing entries, and learn a simple method for constructing magic squares of odd order. The workshop demonstrates that mathematics can be creative, surprising, and enjoyable.
▶ Video 📄 Slides - Talk 10 — Jakob Logan (The University of Texas Rio Grande Valley, USA) — August 9, 2026 | 9:15 AM–9:30 AM (US Central Time)Title: Machine Learning and Philosophy of Science
Abstract
"Godel as Semantic Underdetermination: An Intuitive View of Incompleteness and Machine Learning" This talk hopes to present an intuitive, model-theoretic interpretation of Godel's incompleteness theorems. Rather than treating a Godel sentence only as an unprovable proposition, we can view it as a probe that separates models within the candidate space Mod(T) of a formal theory T. Some models satisfy the Godel sentence, while others satisfy its negation, showing that the theory has not determined a complete semantic profile for the mathematical object it is intended to describe. The aim is expository rather than historically revisionary: much like a 3Blue1Brown-style presentation, the talk will sharpen a visual and conceptual intuition behind established mathematics. It will distinguish determinate truth within a fixed model from underdetermination across admissible models, and explain how strengthening a theory constricts its candidate space without eliminating the recurring Godelian phenomenon. The final portion will connect this perspective to modern machine learning. Learned representations may be internally precise while still failing to distinguish candidate environments that disagree on the intended target. This provides a common language for understanding incompleteness, target underdetermination, context shift, and the limits of synthetic refinement: many of which are increasingly relevant topics in the field of artificial intelligence over the past 3-4 years.
▶ Video 📄 Slides - Talk 11 — Angel Morales (The University of Texas Rio Grande Valley, USA) — August 9, 2026 | 9:30 AM–9:45 AM (US Central Time)Title: Vedic Mathematics
Abstract
This presentation introduces Vedic Mathematics as a collection of mental-calculation techniques that emphasize numerical patterns, complements, base methods, and flexible problem-solving. The talk focuses on how numbers near convenient bases such as 10, 100, and 1000 can be handled through simple cross-addition or cross-subtraction and multiplication of small offsets. Worked examples illustrate rapid multiplication of numbers near a common base, squaring numbers ending in 5, subtraction from powers of 10 using the “all from 9 and the last from 10” method, and the vertical-and-crosswise approach to multiplication. The presentation also highlights the educational value of these techniques in strengthening number sense, pattern recognition, confidence, mental agility, and classroom engagement. Rather than replacing conventional mathematics, the methods are presented as complementary tools that can make selected calculations faster, clearer, and more intuitive for students.
▶ Video 📄 Slides - Talk 12 — Sephora Trevino (The University of Texas Rio Grande Valley, USA) — August 9, 2026 | 9:45 AM–10:00 AM (US Central Time)Title: Recreational Mathematics: Exploring Patterns, Puzzles, Games, and Mathematical Thinking
Abstract
Recreational mathematics presents mathematical ideas through puzzles, games, patterns, and surprising problems that are both enjoyable and intellectually meaningful. This talk introduces several accessible examples, including magic squares, numerical patterns, geometric puzzles, logical challenges, and network-based problems. Each activity demonstrates how curiosity and experimentation can lead to important mathematical concepts such as symmetry, counting, strategy, structure, and proof. The presentation will also show that recreational mathematics is more than entertainment. It encourages creative thinking, careful observation, problem-solving, and the ability to explain mathematical reasoning clearly. Through interactive examples, participants will be invited to make predictions, test strategies, identify patterns, and discover the mathematics hidden inside familiar games and puzzles. The goal of the talk is to demonstrate that mathematics can be engaging, visual, playful, and accessible to students from many academic backgrounds.
▶ Video 📄 Slides - Talk 13 — Tommie Settlemyre (University of North Texas, USA) — August 9, 2026 | 10:00 AM–10:30 AM (US Central Time)Title: A quantum tunneling model of charged particle-antiparticle production in strong electric fields
Abstract
Einstein’s famous relation E=mc^2 suggests that matter is a form of energy, which can be converted to other forms of energy through a dynamical process, as in a nuclear power plant. Relativistic quantum mechanics also allows for energy from fields in empty space to be converted into matter. Namely, quantum fluctuations in strong electric fields can result in the creation of a charged particle together with its corresponding antiparticle. In this work, we develop a Schwinger-inspired quantum tunneling model for production of charged particle-antiparticle pairs obeying the Pauli Exclusion Principle, such as electrons and positrons (anti-electrons). The model is applied to nuclear dynamics in stars. We find that the production of electron-positron pairs may act as a catalyst for the fusion of light ions in the cores of stars, which makes the creation of heavier elements possible. Time permitting, we will apply the model to the alpha decay of light ions, and compare with some preliminary experimental results.
▶ Video 📄 Slides - Talk 14 — Saidat Yusuff (Auburn University, USA) — August 9, 2026 | 10:30 AM–11:00 AM (US Central Time)Title: Shared Gap Optimization of Valley-Hall Photonic Crystals
Abstract
Valley-Hall photonic devices are realized by interfacing two photonic crystals possessing opposite valley topological characteristics while sharing a common bulk band gap. Although conventional photonic band-gap optimization typically focuses on a single photonic crystal, optimizing each crystal independently does not guarantee a common operating frequency range after optimization. This work develops a computational framework for simultaneously maximizing the shared gap-midgap ratio of two two-dimensional valley-Hall photonic crystals under transverse-magnetic (TM) polarization. The out-of-plane magnetic field is modeled by the scalar TM Maxwell eigenvalue problem with Bloch-periodic boundary conditions on a primitive unit cell. The governing equations are discretized using continuous piecewise-linear finite elements, yielding a parameter-dependent generalized eigenvalue problem. The inverse-permittivity distributions of both photonic crystals are optimized simultaneously using a sequential semidefinite-programming (SDP) framework. Projected matrix inequalities constrain the lower and upper band edges of both crystals, while a Charnes–Cooper transformation converts the fractional shared gap-midgap objective into a convex optimization problem. A trust-region strategy controls the accuracy of the local spectral approximation and determines acceptance of each design update through repeated solution of the nonlinear eigenvalue problem. The proposed optimization and topological analysis framework provides an effective computational methodology for designing valley-Hall photonic crystals with enlarged shared operating gaps while preserving the opposite valley topology required for robust interface-state propagation. By integrating finite element analysis, semidefinite programming, and topological characterization within a unified computational framework, this work provides a systematic approach for the design and optimization of topological photonic materials.
▶ Video 📄 Slides - Talk 15 — Md Mehedi Hasan Bhuiyan (University of Central Florida, USA) — August 9, 2026 | 11:00 AM–11:30 AM (US Central Time)Title: Topological Characterization of Global Physiological Biomarkers Dysregulation in Older Adults Among Type II Diabetic
Abstract
Type 2 diabetes is a major metabolic disorder disease and a growing public health burden, especially among middle-aged and older adults. Biologically, Type 2 diabetes develops through progressive insulin resistance and deterioration of pancreatic β-cell function, ultimately leading to chronic hyperglycemia and widespread metabolic dysregulation. It is usually studied through individual biomarkers such as glucose, HbA1c and lipids profile. However, diabetes may also change the global organization among these biomarkers. This study investigates systemic metabolic alterations among individuals aged over 50 years by comparing diabetic and non-diabetic groups across multiple physiological domains, including glycemic regulation, lipid metabolism, adiposity, cardiovascular function, inflammation, and renal metabolic activity. We used data from the National Health and Nutrition Examination Survey (NHANES) 2009–2010, 2017–2018, and August 2021–August 2023 cycles. Participants were categorized as diabetic and nondiabetic group. We applied complementary statistical and topological methods to characterize differences in the physiological and metabolic profiles of diabetic and non-diabetic groups. The results demonstrate that Type 2 diabetes is not merely associated with abnormalities in isolated individual biomarkers but reflects a large-scale systemic reorganization of physiological structure. Diabetic groups consistently exhibit reduced topological complexity and weaker multivariate coordination compared with non-diabetic controls, indicating disruption of integrated metabolic homeostasis. Overall, these findings suggest that global metabolic dysfunction in Type 2 diabetes represents a holistic structural breakdown of interconnected physiological systems, which may contribute to increased risks of cardiovascular disease, multi-organ complications, morbidity, and mortality.
▶ Video 📄 Slides - Talk 16 — Piyali Chakraborty (University of Central Florida, USA) — August 9, 2026 | 11:30 AM–12:00 PM (US Central Time)Title: Spectral Pairs and their relation to tiling set in \mathbb{R}^{d}
Abstract
We present a class of unbounded subsets of R^{d} for which the Fourier transform satisfies a Plancherel identity with respect to an explicit pair measure. We characterize these spectral pairs in terms of translation tilings by lattices and finite sets, extending classical results of Fuglede and Pedersen to periodic unbounded domains. This talk is based on joint work with my supervisor Dr. Dorin. E. Dutkay.
▶ Video 📄 Slides - Talk 17 — DIPOK DEB (University of Central Florida, USA) — August 9, 2026 | 12:00 PM–12:30 PM (US Central Time)Title: Linear Programming Optimization using Explicit and Implicit Deep Learning Model.
Abstract
Linear programming (LP) is an important class of optimization problems with applications in operations research, signal processing, business management, and many other fields. In learning to optimize (L2O), machine learning and deep learning models can be trained to predict an initial solution or an approximate optimal solution. These predictions can either solve an optimization problem directly or guide classical optimization algorithms. Explicit and implicit deep learning models have also gained significant attention in machine learning. In this work, we construct an explicit graph neural network (GNN) that maps LP instances of bounded size to corresponding outputs. To validate the proposed approach, we train a simple GNN and evaluate its ability to predict the feasibility and solutions of LP instances. We also develop an implicit GNN for solving LP problems and compare the performance of explicit and implicit models.
▶ Video 📄 Slides - Talk 18 — Claudia Maria Schmidt (Washington State University at Pullman, USA) — August 8, 2026 | 11:00 AM–11:30 AM (US Central Time)Title: Towards a Preliminary Research Proposal: Connecting Complex Analysis and Algebra through Category Theory
Abstract
We wish to contribute to establishing Category Theory as unified framework for pursuing all mathematics by in particular investigating deep connections between Algebra and Complex Analysis through a Categorial lens.Three strands of possible connections are considered: 1.) As a well-known example for information flowing form Complex Analysis to Algebra we examine L-functions, which are constructed in specific ways from certain Algebraic Curves, and by that construction and by the properties of the underlying Algebraic Curve, reveal properties of the related algebraic objects. The most famous example is the complex Riemann Zeta function and its analytic continuation, which encodes through the location of its nontrivial zeros information about the distribution of prime numbers to prove the prime number theorem. We want to formulate the respective relations in terms of Functors. 2.) We want to recover in Categorical terms those established theorems from Complex Analysis that underlie the results of point 1, in particular the location of zeros and the relations between zeros, poles and winding number. 3.) We investigate also the flow of information from Algebra to Complex Analysis. We ask, as an example, if the Algebraic Curves defined by polynomial formulas for (certain) primes established so far, by polynomials like Mersenne primes, Fermat primes, or Fibonacci primes or the recent attempt of Tao et al. to establish a general polynomial formula, by themselves reveal also interesting Differential Geometric and therefore Complex Analytic Properties - such as the related curvature or the possibility of the quadrature of integrals by the polynomial, or a resulting Moduli Space (the Quotient of a Manifold and the Diffeomorphisms on it) - that can be reframed in Categorial terms.
▶ Video 📄 Slides