About Me 

My name is Blake Bates, and I am a PhD student in Applied Mathematics at the University of Arizona. My research focuses on the intersection of Topological Data Analysis (TDA), signal processing, and machine learning. 

I am particularly interested in understanding how geometric and topological structure in signal embeddings relates to properties of the original signal. My current work studies persistent homology of delay-coordinate embeddings, robustness of persistence-diagram representations, and machine-learning surrogates for accelerating topological computations. 

In my free time, I enjoy running and hiking. 

Education and Background 

I completed my undergraduate degree in Mathematics at the University of Minnesota, followed by a Post-Baccalaureate program in Mathematics at Iowa State University. I then earned a Master's degree in Applied Mathematics at the University of Arizona, where I developed a stronger background in computational mathematics, data analysis, and mathematical modeling. 

Professional Experience and Teaching 

I have professional experience in signal processing and modeling at Raytheon, where my work has included the application of mathematical, computational, and machine-learning methods to signal-processing problems. 

In academia, I have taught undergraduate mathematics courses including College Algebra and Calculus II, and I have also served as a Super-TA for MATH 581: Methods of Applied Mathematics. These experiences have strengthened my interest in teaching, mentoring, and communicating technical ideas clearly. 

Research Interests and Aspirations 

My current research explores how topology can provide useful representations of signals, how spectral and dynamical properties are reflected in persistent homology, and how machine learning can make topological methods more computationally practical. I am especially interested in developing mathematically grounded methods that connect signal structure, geometry, topology, and computation. 

Long term, I am interested in research roles in academia, national laboratories, or industry involving applied mathematics, signal processing, TDA, and machine learning.