ALEJANDRO PARADA-MAYORGA

I develop the mathematical foundations that reveal how information processing systems work across radically different domains—from social networks to power grids to quantum computers. By uncovering the fundamental algebraic structures these systems share, I build theory that explains why modern machine learning architectures succeed and design new systems that are more reliable, explainable, and efficient.

I am a Tenure Track Assistant Professor in the Electrical Engineering Department at the University of Colorado Denver. Previously, I was a postdoctoral researcher and research scientist at the University of Pennsylvania, where I worked on Algebraic Signal Processing and the Mathematical Foundations of Deep Learning. I received my Ph.D. in Electrical Engineering from the University of Delaware.

My research addresses a central challenge in modern information science: understanding the universal properties of information processing systems on arbitrary domains. Despite geometric and topological differences between domains—graphs, manifolds, point clouds, or discrete structures—many share fundamental algebraic structure. This observation drives my work. By leveraging tools from representation theory, algebraic geometry, algebraic topology, and category theory, I develop principled approaches to sampling, filtering, pooling, and stability analysis that apply broadly across domains.

This work has direct implications for critical applications. In large networked systems, my graphon-based frameworks enable optimal solutions to computationally expensive problems that transfer across network scales. In machine learning, my algebraic approach to convolutional neural networks provides theoretical guarantees for stability and generalization. In signal processing, my methods yield provably optimal sampling strategies for complex network data.

I lead this research program as founder and director of the Abstract Signal Processing Lab (ASP Lab) at CU Denver, where we pursue fundamental questions at the intersection of algebra, geometry, and learning theory.