I am a tenure-track Assistant Professor of Electrical Engineering at the University of Colorado Denver, where I founded and direct the Abstract Signal Processing (ASP) Lab. My research is organized around a single thesis: algebraic structure is what ultimately determines when and why signal processing systems transfer across domains. Geometric and data-driven approaches capture a great deal about these systems, but the transfer question itself is answered at the algebraic level. Algebraic Signal Processing is the framework through which I pursue this thesis, and it sits at the core of every problem I study.
The question is a fundamental one in modern information science. A filter designed for a power grid, a neural network trained on social data, a sampling strategy derived for a manifold: under what conditions do these generalize, and what guarantees can we give? This is not a question about fine-tuning models or adapting datasets. It is a structural question, and my work rests on the answer being algebraic — transferability is not an empirical accident but a property determined by the algebraic relationships between domains. Making this precise yields a theory that is predictive rather than merely descriptive, and that leads to systems that are reliable, explainable, and efficient by design.
The observation driving this program is that domains with radically different geometry and topology — graphs, graphons, manifolds, quivers, discrete structures — often share deep algebraic structure, and that shared structure is precisely what makes transfer possible. Using tools from operator algebras, representation theory, graphon theory, and category theory, I develop rigorous frameworks for sampling, filtering, pooling, and stability analysis that are transferable across domains by construction, not by hope.
This approach has direct consequences for hard problems. In large networked systems, graphon representations let me characterize the optimality conditions of sampling sets on graphs at massive scale; the same structure identifies which degrees of freedom in a large network carry information at all, which I have applied to dimensionality reduction. In machine learning, my algebraic theory of convolutional architectures provides stability and generalization guarantees that purely empirical methods cannot. In signal processing, a theory of uniqueness sets grounded in operator algebras extends classical sampling theorems to arbitrary domains and yields optimal sampling strategies for complex network data.
At the ASP Lab, we pursue these questions at the intersection of algebra, geometry, and learning theory, building the mathematical foundations that make transferable intelligence principled and provable.
Short Bio: Before joining CU Denver, I spent five years at the University of Pennsylvania as a postdoctoral researcher and research scientist in Alejandro Ribeiro’s group, where I began extending Algebraic Signal Processing into a rigorous mathematical foundation for deep learning. That work includes foundational results on the stability of algebraic neural networks to deformations, showing that the invariance and stability properties long observed empirically in convolutional architectures are consequences of underlying algebraic structure rather than incidental to it. I received my Ph.D. in Electrical Engineering from the University of Delaware, where I worked on the general theory of sampling in compressed sensing and graph signal processing.
