2026 Texas High School Mathematics Research Conference @TAMU
May 2nd to May 3rd, 2026
May 2nd to May 3rd, 2026
Location: TAMU Blocker Building (Room 117)
Schedule on May 2nd:
Presentation Schedule
9:00 am --- 9:10 am
Welcome by Dr. Kun Wang (Director of PReMa program, TAMU)
9:10 am --- 9:50 am Plenary Talk
Dr. Michael Willis (Assistant Professor, TAMU)
9:55 am --- 10:10 am
Priya Viswanath (Lebanon Trail High School)
Mentors: Dr. Wencai Liu, Dr. Xueyin Wang, Sebastian Vargas Loaiza
10:15 am --- 10:30 am
Ayush Narayan (Walnut Grove High School)
Mentors: Dr. Wencai Liu, Dr. Xueyin Wang, Sebastian Vargas Loaiza
10:35 am --- 10:50 am
Neev Shaw (Stanford Online High School)
Mentors: Dr. Wencai Liu, Dr. Xueyin Wang, Sebastian Vargas Loaiza
10:55 am --- 11:10 am
Aanya Gupta (Stanford Online High School)
Mentors: Dr. Xin Liu
11:15 am --- 11:35 am
Max Tang (John Burroughs School)
Mentors: Dr. Wencai Liu, Dr. Xueyin Wang, Sebastian Vargas Loaiza
11:40 pm --- 12:00 pm
Alex Chen (Shady Side Academy)
Mentors: Dr. Wencai Liu, Dr. Xueyin Wang, Sebastian Vargas Loaiza
12:00 pm --- 1:00 pm Lunch Break
1:00 pm --- 1:10 pm Poster
Aanya Gupta (Stanford Online High School)
Mentors: Dr. Xin Liu
1:10 pm --- 1:25 pm
Emily Mei (The Kinkaid School )
Mentors: Dr. Wencai Liu, Dr. Xueyin Wang, Sebastian Vargas Loaiza
1:30 pm --- 2:00 pm
Kevin Hu (Clements High School) and Helen Gou (Dulles High School)
Mentor: Dr. Xiaoxi Shen (Texas State University)
2:05 pm --- 2:20 pm
Samuel Gu (A&M Consolidated High School)
Mentors: Dr. Sherry Gong, Dr. Michael Willis, Dr. Qiaochu Ma
2:25 pm --- 2:40 pm
Steven Ning (Friendswood High School)
Mentor: Dr. Xin Liu
2:45 pm --- 3:05 pm
Prisha Aswal (Willamette Valley Academy)
Mentors: Dr. Zhizhang Xie and Dr. Runjie Hu
3:05 pm --- 3:30 pm
Certification Ceremony
Title and Abstract:
Title: Recycling Collection in Grid Cities: A Mathematical Framework for the Drop-Off Systems
Presenter: Aanya Gupta (Poster)
Abstract: We develop a mathematical framework to evaluate and optimize residential recycling collection in grid-structured cities. While curbside collection and centralized drop-off recycling centers are widely used, their relative cost-effectiveness depends on city geometry, population distribution, and operational constraints. We model a city as a parameterized grid defined by its dimensions, street spacing, and population density, allowing real-world cities to be approximated. Within this framework, we construct models for both curbside pickup and drop-off recycling centers. For recycling centers, we model grid-based “neighborhoods,” incorporate distance-dependent participation rates, and determine the number and cost of facilities required for full city coverage. We introduce effectiveness functions that combine economic cost and participation-adjusted satisfaction, enabling direct comparison between the two systems. Our results demonstrate how optimal strategies depend on city scale and density, and show that while curbside pickup maximizes participation, well-placed recycling centers can significantly reduce costs in lower-density settings.
Title: Twisting Braids with Group Theory: Cryptography Future beyond Primes
Presenter: Ansh Gupta
Abstract: As quantum computers approach reality, the digital security of our global financial and private data faces a crisis. Current encryption relies on large integer factorization tasks normal computers cannot handle, but one that Shor's Algorithm can solve nearly instantaneously. This weakness necessitates a new standard of quantum - resistant cryptography. This project explores non- abelian group theory - based cryptography specifically, Braid Groups as a versatile alternative based on the Conjugacy Search Problem ( CSP ). This system is complex even for quantum computers, as it involves strings representing information getting tangled in random, unpredictable ways that lack the periodic structure required for a Shor - style attack. Two Python programs were written: a "Searcher" to simulate encryption and a "Hacker" to simulate a brute - force decryption attempt. Execution times were measured over various braid orderings ( B4, B5, B7 ) and the number of string crossings in a braid rising. Due to time constraints, testing very large keys was impossible; therefore, projections were made on a logarithmic scale to show where decryption becomes impossible for even the fastest computers utilizing Grover's Algorithm for quantum search acceleration. Results showed that brute - force decryption time increased exponentially while encryption time stayed consistently low. This produced a significant "complexity gap," proving that Braid Groups offer a strong barrier against unwanted access. Ultimately, the findings imply that non - abelian group theory provides a safe foundation for post - quantum cryptography, as it remains computationally infeasible for even high - speed processors to crack because the quadratic speedup of quantum search is insufficient to overcome the exponential growth of the braid's configuration space.
Title: Quantifying Electron Movement: Exploring Disorder and Localization in Quantum Systems
Speaker: Priya Viswanath
Abstract: This presentation introduces the physical and mathematical foundations of electron movement, focusing on the transition between conducting metals and insulating materials. While traditional models assume perfect crystalline order, real-world materials contain impurities that create disorder. We explore how this disorder affects the motion of electrons, transitioning from a state of delocalization, where an electron wave spreads freely, to localization, where it becomes confined to one place. This setup bridges the gap between theoretical quantum mechanics and practical materials science, providing the necessary context to understand why disorder is the key to modern electronic behavior like designing more efficient LEDs.
Title: Quantum Mechanical Foundations of Localization in Discrete Systems
Speaker: Ayush Narayan
Abstract: This presentation discusses the use of the quantum-mechanical framework to model a particle's behavior in a lattice-based system. Unlike classical particles, electrons move by wave functions, where the square of the amplitude represents the probability of finding the particle at a given position. We consider a spatial model in which the positions are represented by a dynamics governed by the Schrodinger equation. The system uses the Hamiltonian operator composed of a Laplacian. This helps us study how quantum states evolve over time and helps us understand the basis for localization and delocalization in materials.
Title: The Discrete Schrödinger Framework for Electron Localization in Disordered Systems
Speaker: Neev Shaw
Abstract: This talk develops the discrete Schrödinger framework for electron localization on a lattice with disordered potential. We first define the Hamiltonian matrix that indicates the total energy landscape of the lattice including both potential energy and the discrete Laplacian. We then investigate how an initially localized wave function evolves, and how different potentials impact the spread of the electron and can induce localization or delocalization. The central aim is to connect numerical evolution with spectral theory to rigorously classify transport in disordered quantum systems.
Title: Spectral Methods for Analyzing Localization in Disordered Quantum Systems
Speaker: Emily Mei
Abstract: This presentation explores how spectral methods can be used to understand the behavior of quantum particles in disordered lattice systems. Rather than directly tracking the full time evolution of a particle’s wave function, we study how the system can be decomposed into fundamental stationary components and how these components contribute to transport across the lattice. By examining how different parts of the system are connected and how this behavior changes under randomness, we develop a framework for distinguishing between spreading and localization. This approach highlights how underlying spectral properties of the system govern whether a particle remains confined or is able to propagate over long distances.
Title: Measuring Localization in the One-Dimensional Anderson Model
Presenter: Alex Chen, Max Tang
Abstract: It is well known that the one-dimensional Anderson model, consisting of the discrete Laplacian plus a random potential, exhibits localization: waves do not spread freely but remain trapped in a bounded region around random centers. In this talk, we use Python to measure localization quantitatively in finite tridiagonal matrices with several choices of random potential — Bernoulli on {0,1}, ternary on {0, 1/2, 1}, and continuous uniform on [0,1]. For each, we compute a boundary-to-boundary transmission E(Q) both exactly (by enumerating all 2^N disorder configurations for N ≤ 25) and via Monte Carlo sampling (for N up to 100). The decay rate of E(Q) as the chain grows gives a quantitative measure of the localization length. Moreover, it was observed that the exponential decay rate 𝛾 was proportional to the variance of each Bernoulli independent variable with proportionality constant 1/10. Finally, continuous sweep over the Bernoulli probability p traces the predicted parabola p(1-p)/10 across 19 sample values. We will discuss both the underlying mathematical setup and the numerical experiments.
Title: Computational Biomechanical Framework for Kathak Injury Risk Analysis: Weight Shift Dynamics & Meniscal Tensile Fatigue
Presenter: Aanya Gupta
Abstract: Dancers are susceptible to a variety of injuries due to repetitive motion and physical strain, with 8 in 10 dancers getting injured each year and 72% of injuries occurring below the Ultimate Tensile Stress (Callahan et al.). Studies report approximately 0.6–5 injuries per 1,000 hours of dance exposure, largely due to repetitive loading, deep knee flexion, and high-impact transitions. Kathak dancers are particularly vulnerable to meniscal damage from constant axial loading and rapid pivots. This project develops a computational biomechanical model of a Kathak dancer’s lower body to analyze how joint constraints influence movement efficiency and injury risk. Using the Wolfram Language, I constructed a kinetic chain model of the hip, knee and ankle, incorporating anatomical joint limits and rule-based safety constraints. Forward and inverse kinematics was applied to simulate transitions between poses, where inverse kinematics was used to produce more anatomically realistic animations. An efficiency metric minimized joint variation and angular stress between sequential poses. Additionally, a mathematical tensile fatigue model simulated repetitive loading and stress accumulation within the meniscus caused by tensile fatigue. Results show that mathematically constrained pathways reduce excessive joint strain and eliminate oscillatory or unstable transitions. Overall, this research demonstrates that computational biomechanical modeling provides a low-cost, non-invasive method to analyze dance movement and injury mechanisms. Future work includes refining the meniscus tear model to be predictive, incorporating recovery-based rehabilitation variables, mapping tension distribution across dance surfaces, validating results with real-world dancer data to enhance injury prevention strategies, and further investigating the location of perturbations within the meniscus model.
Title: Evaluating Naive Bayes Classifiers with Synthetic Data in Machine Learning
Presenter: Kevin Hu and Helen Gou
Abstract: We explore several important extensions of the Naive Bayes classifier and their applications in classification problems. The featured models are the tree-based classifiers TAN and Hie-TAN, the averaged one-dependence estimators AODE and WAODE, and a Hybrid Logistic Regression–Naive Bayes classifier, with Logistic Regression included as a benchmark comparison model. We will also review prerequisite concepts such as Bayes’ Theorem, conditional probability, ROC curves, and common performance metrics used in machine learning.
Title: Investigating the Strength of Eisermann’s Modulo 32 Ribbon Obstruction
Presenter: Samuel Gu
Abstract: Determining if a link is ribbon is a central problem in geometric topology. While classical algebraic obstructions, such as vanishing linking numbers $\ell k=0$, zero signature $\sigma=0$, and the Fox-Milnor condition, are used to identify slice suspects, Eisermann recently introduced a modern necessary condition based on a modulo 32 congruence. This project investigates whether this condition is strictly stronger than the classical suite for multi-component links. We conducted a computational sweep of over 30,000 links using SnapPy and SageMath, analyzing the 14-crossing and 15-crossing datasets. We sought "imposters" that satisfy classical algebraic sliceness but fail the Modulo 32 test. No counterexamples were found; all 357 suspects at 15 crossings satisfied the condition and were verified as ribbon. We also developed an analytic framework for the 2-component case, providing evidence that for low-complexity links, classical criteria may be sufficient to satisfy this modern obstruction.
Title: Optimizing Curbside Pickup Recycling Methods in a Grid City
Presenter: Steven Ning
Abstract: In this study, we analyze and compare two widely used recycling methods: curbside pickup and recycling center drop-off. We optimize recycling logistics in grid-based cities, emphasizing both service satisfaction and cost efficiency. This presentation focuses specifically on the curbside pickup approach, where we incorporate traffic conditions and truck movement into a grid-based framework for coverage optimization and route planning.
Title: Is Area a Sufficient Condition for Scissors Congruence?
Presenter: Prisha Aswal
Abstract: Scissors congruence is the geometric notion that two polygons are congruent if one can be cut into finitely many pieces and reassembled to form the other. We demonstrate the Wallace-Bolyai-Gerwien Theorem, showing that every polygon can be decomposed into triangles and then subsequently reduced to rectangles with a unit-width edge using shearing and parallelogram transformations. When scaling to three dimensions, we show why equal volume is no longer sufficient for congruence. By using Dehn’s invariant, we get
the additional quantity needed to classify the 3D dissection, resolving Hilbert’s Third Problem. We conclude by connecting these
ideas to the Four-Color Theorem.
Schedule on May 3rd
Free discussion with your mentors
Campus visit