Blake Bates

Ph.D. Student in Applied Mathematics University of Arizona Tucson, Arizona [email protected]

Research Interests

Topological Data Analysis, signal processing, persistent homology, delay-coordinate embeddings, computational topology, machine learning, surrogate modeling, and numerical methods.

Education

University of Arizona Ph.D. in Applied Mathematics, expected May 2028

University of Arizona M.S. in Applied Mathematics, May 2025

Iowa State University Post-Baccalaureate Mathematics, May 2023

University of Minnesota B.S. in Mathematics, December 2021

Professional Experience Systems Engineer II, Signal Processing

Raytheon | January 2026–Present

Develop Python and C++ software for modeling, simulation, signal processing, and algorithm development. Apply signal processing, machine learning, Topological Data Analysis, and mathematical modeling to research and development problems. Develop computational and GPU-based simulation workflows. Analyze interferometric and time-series data using Fourier methods, filtering, statistical analysis, and custom algorithms. Served as primary inventor of proprietary technology designated as a Raytheon trade secret in July 2026. Data Analyst

Duke Cannon Supply Co. | October 2020–August 2022

Conducted data analysis and financial reporting in collaboration with the CFO. Automated recurring reporting and analysis workflows. Research Experience Doctoral Researcher, Topological Signal Processing

University of Arizona | 2024–Present

Study connections among signal processing, delay-coordinate geometry, persistent homology, and machine learning. Investigate how spectral properties of signals are reflected in the topology of delay-coordinate embeddings. Study analytical relationships between sinusoidal frequency, delay phase, ellipse geometry, and (H_1) persistence. Compare persistence-diagram representations with respect to predictive utility and robustness under signal perturbations. Investigate machine-learning surrogate models for approximating persistence quantities and reducing computational cost. Develop Python pipelines for sliding-window embeddings, persistent homology, persistence representations, Fourier analysis, and numerical studies. Research Assistant, Signal Processing and TDA

University of Arizona / Raytheon SPARK Program | May 2024–December 2025

Applied signal processing and TDA to defense-related research problems. Developed pipelines for Fourier analysis, filtering, autocorrelation, periodicity detection, and analysis of interferometric and time-series data. Presented technical results to researchers and engineers. Research Assistant, National Security Programs

University of Arizona | January 2025–May 2025

Developed machine-learning and natural-language-processing methods for analyzing grant proposal trends and funding alignment. Applied text embeddings, statistical learning, and predictive modeling to proposal data. Researcher, Topological Analysis of Aluminum Alloys

University of Arizona | May 2024–August 2024

Applied TDA and clustering methods to materials data to identify structural similarities among aluminum alloys. Undergraduate Researcher, Anti-Ramsey Theory

University of Minnesota | May 2021–August 2021

Conducted combinatorics research using analytical and computational methods. Research resulted in a peer-reviewed publication in Involve, a Journal of Mathematics. Publication

Bates, B., Berikkyzy, Z., Chiem, N., Elvin, G., Fines, R., Lie, M., Mikulás, H., Reiter, I., and Zhou, K. “Bounds for Rainbow-uncommon Graphs.” Involve, a Journal of Mathematics, 19 (2026), 249–257.

Teaching Experience Graduate Teaching Instructor / Teaching Assistant

University of Arizona | August 2023–December 2024

Instructor of record for College Algebra. Developed course materials, delivered instruction, and supported undergraduate students. Teaching Assistant

Iowa State University | August 2022–May 2023

Led recitations and review sessions for courses ranging from College Algebra through Calculus II. Technical Skills

Programming: Python, C++, Git, GPU computing

Scientific Computing: NumPy, SciPy, Pandas, Scikit-learn, Matplotlib

Topological Data Analysis: Persistent homology, Vietoris–Rips complexes, persistence images, persistence landscapes, Mapper, sliding-window embeddings, delay-coordinate embeddings

Machine Learning: Random forests, XGBoost, regression, classification, dimensionality reduction, feature engineering, surrogate modeling

Signal Processing: Fourier analysis, digital filtering, autocorrelation, periodicity detection, interferometric data analysis, time-series analysis

Mathematics: Computational topology, numerical methods, probability, optimization, functional analysis, complex analysis