CV
PDF versions: Concise resume · Full academic vita
Education
- Ph.D. in Mathematics, Princeton University, 2001. Thesis advisor: Peter Sarnak.
- B.Sc. in Mathematics, University of Guanajuato, Mexico, 1996
Professional Employment
- Research Consultant, Gibran.ai (AI startup; seed funding from Together Fund), 2025–2026. Full-time research consulting, June-December 2025.
- Associate Professor, The University of Texas at San Antonio, 2011 – Present
- Assistant Professor, The University of Texas at San Antonio, 2005–2011
- Presidential Fellow, The University of Texas at San Antonio, 2004–2005
- J. J. Sylvester Assistant Professor, The Johns Hopkins University, 2002–2004
- Research Fellow, American Institute of Mathematics, Palo Alto, 2001
Research Awards & Grants
- NSF Grant: "Model Theory and Ergodic Theorems" (2015–2019). Co-PI with José N. Iovino.
- AMS/Tensor-SUMMA Grant (2007–2008). Supported UTSA’s Problem-Solving Seminar.
Research Interests
My research revolves around analysis in a broad sense. I have worked on random matrix theory (Dyson’s “Threefold Way”; linear group ensembles) and number theory (zeros of L-functions); nowadays, my research is on the foundations of analysis and probability, as well as both theoretical and applied aspects of real-valued computing.
- Measure, integration, probability, and information theory
- Real-valued computability (deterministic, randomized, and quantum)
- Statistical/machine learning and AI foundations
Publications
Refereed papers and preprints — see the full list on the Publications page.
Talks
Research and outreach talks and short courses — see the Talks page.
Teaching
Courses taught, by term — see the Teaching page.
Mentorship
Master’s Theses
- Zachery Sharon, UTSA (2011). An Explicit Proof of the Weak Finite Basis Theorem and Applications to Computing Ranks of Elliptic Curves
- Elkin O. Quintero Vanegas, Universidad Nacional de Colombia (2011). La Fórmula del Número de Clases y Valores Especiales de Funciones-L: Desde Dirichlet y Dedekind hasta Stark
Undergraduate Theses
- Julio C. Galindo López, UNAM (2013). Matrices Aleatorias y Funciones-L
- Dal S. Yu, UTSA (2011). Representation Theory of Classical Compact Lie Groups
Academic Synergy
- Faculty mentor, UTSA Problem-Solving Club (since 2006)
- UTSA Faculty Liaison to the Putnam Competition (since 2006). UTSA ranked top 8% nationwide in 2015.
- Academic coach/mentor, AAAS Olympiad program (since 2012). Mentor/coach of 20 students from underrepresented communities in mathematics.
Professional / Editorial Service
- Associate Editor, Mathematics Magazine (2016–2019)
- Co-editor, Problems and Solutions column, Mathematics Magazine (2016–2019)
- Co-organizer (with J. Iovino), session "Topological Methods in Model Theory", Meeting of the AMS Central Section, University of Texas at San Antonio (2024)
- Reviewer of manuscripts for Princeton University Press, Oxford University Press
- Referee. Annals of Pure and Applied Logic, Bulletin of the London Mathematical Society, Communications in Mathematical Physics, Experimental Mathematics, Journal of Number Theory, Journal of Physics A, Mathematics Magazine, The Ramanujan Journal, Indian Journal of Mathematics, Random Matrices: Theory and Applications, and others.
- NSF panelist; proposal reviewer for CONACyT (Mexico)
- Judge of student abstracts and posters, SACNAS (2010–2018)
Professional Memberships
- American Mathematical Society (AMS)
- Mathematical Association of America (MAA)
- Association for Symbolic Logic (ASL)
- Society for Advancement of Chicanos and Native Americans in Science (SACNAS)