Alvaro Arias

Welcome to my academic homepage. I am a Professor of the Department of Mathematics at the University of Denver, where I have been a faculty member since 2001. I currently serve as Chair of the department. My path in mathematics has taken me from Central America to the United States to the Middle East, beginning with my undergraduate studies in mathematics at Universidad del Valle de Guatemala, followed by my master's and PhD degrees from Texas A&M University.

My postdoctoral training included the Weizmann Institute of Science in Israel and Case Western Reserve University. Before joining the University of Denver, I served as a faculty member at the University of Texas at San Antonio, where I rose through the ranks to become a full professor.

My research in mathematics has focused mainly on Functional Analysis, particularly in Banach spaces and Operator Algebras. I was fortunate to study at Texas A&M University, which at the time was a leading center in the local theory of Banach spaces, probability in Banach Spaces and Operator spaces.  During my time there, I learned many techinques, like concentration of measure phenomena, Gaussian processes and non-parametric techniques, which have become central in machine learning, and high-dimensional probability and statistics. 

My most cited papers are in non-selfadjoint operator algebras, specifically in non-commutative interpolation problems, that are modeled on Fock spaces. I have also published articles in Banach spaces, Convex Geometry, Operator Spaces, C* algebras, Ramsey Theory and Quantum Computing. Recently, like many others in our field, I've developed an interest in Machine Learning and its theoretical foundations, where I hope my background in functional analysis might be useful.