About me

The short version

A native of Guadalajara, Mexico, I am a mathematician trained in analysis and number theory. My research has included random matrix theory and analytic number theory, but has shifted towards the foundations of analysis, probability, and computation —with a growing interest in applications to artificial intelligence. I am faculty at UT San Antonio and have started consulting for the AI industry.

Research and explorations: what I enjoy thinking about

If there is a single thread running through my interests, it is a fondness for broad, general patterns —the structures that recur across very different subjects once you squint.

As an analyst, some of the fundamental questions I ponder pertain to measure and integration, probability and information, and the theory of real-valued and continuous logics. Continuous logic is a network connecting analysis with model theory; real-valued logic, in particular, underlies contemporary AI. I know my way around computer code: a skill that serves me as researcher, teacher, and AI consultant of late.

I also very much continue to enjoy recreational problem-solving. Nothing I love more than a problem that forces you to understand something you know a little better, to learn something new to solve it, or to connect a little question to bigger ones.

Teaching: what it means to me

As much as I enjoy thinking about and learning mathematics, the human and cultural aspects of the discipline are just as important. I take my role as educator to heart and like to push at curricular boundaries, try new pedagogical approaches, and hold students to high standards they can meet. I will mentor any students having a sincere desire to learn and the discipline and drive to go along with the hunger for knowledge; nevertheless, opportunities to work with students from non-traditional, underprivileged or similar backgrounds to mine are specially meaningful. My acknowledgments give context to these values I hold as a teacher.

Over the years, I have mentored hundreds of students entering math competitions as well as UTSA’s Putnam team for the better part of two decades. I do spend the occasional hour or two figuring out an interesting competition problem with my students —or by myself.