- Supporting Student Learning and Success in Early Undergraduate Mathematics Courses via AI-Enhanced Education (PI Gutiérrez), 2026-2029m $374k, NSF Award 2518973.
- NIH R25: Training Biomedical Research Teams for Rigor and Reproducibility in Data Science (PI Gutiérrez, PI Liu), 2023-2028m $425k (UTSA) out of $4.25M (total), NIH contract 1R25GM151182.
- Technologies for Host Resilience – Host Acute Models of Malaria to study Experimental Resilience (THoR’s HAMMER) (Co-PI Gutierrez, co-PI Tirouvanziam, PI Galinski) , 2016-2019, $1.9M subaward out of $6.5M, DARPA contract contract W911NF-16-C-0008, 2016-2019.
- ALICE (Adaptive Learning for Interdisciplinary Learning Environments) (PI Gutierrez, co-PI Arnold, co-PI Portes) , 2016-2018, $299K, NSF award 1645325.
- Collaborative Research: NSF INCLUDES: An Integrated Approach to Retain Underrepresented Minority Students in STEM Disciplines (Co-PI Gutierrez, PI Barbour), 2016-2018, $117K, NSF award 1649226.
- MaHPIC (Malaria Host-Pathogen Interaction Center) (Co-I Gutierrez, PI Galinski), 2012-2017, $19M, MaHPIC, NIAID contract HHSN272201200031C.
- International Centers of Excellence in Malaria Research (ICEMR) – Center for non-Amazonian regions of Latin America (CLAIM) (Co-I Gutierrez, PI Herrera), 2011-2017, $140K subaward out of $5.5M, NIAID cooperative agreement U19AI089702-01.
- Modeling dispersal of invasive snail species in Florida. Florida Department of Agriculture, Division of Aquaculture. 2008, $2,500 PI Gutiérrez). This project created a reaction-diffusion model to predict the dispersal of apple snails (Pomacea canaliculata) across the state of Florida.
- (PI Borràs, PI of subaward Gutiérrez) DISCOVER-LIT. Sub-award from contract TSI-070300-2008- 67, funded by the Spanish Ministry of Industry. This project intended to create an information system based on the Literatronica engine to allow visitors in the City of Barcelona to get lost in the discovery of the city. 2008-2009, $100K sub-award out of a $300K research contract.
- Contravía (Counterway) (PI Gutiérrez). Award # IDCT-410/1998 by the Instituto Distrital de Cultura y Turismo de Bogotá (Institute of Culture and Tourism of the City of Bogota) to develop the Literatronica system. 1998-1999, $12K
- Condiciones Extremas (Extreme Conditions) (PI Gutiérrez). Award # IDCT-514/1997 by the Instituto Distrital de Cultura y Turismo de Bogotá (Institute of Culture and Tourism of the City of Bogota) to write the experimental electronic novel Condiciones Extremas. 1997-1998, $30K.
- El Primer Vuelo de los Hermanos Wright (The First Flight of the Wright Brothers) (PI Gutiérrez). Award # COLCULTURA-SECAB 014/1996 by the Instituto Colombiano de Cultura – Colcultura, now the Ministry of Culture (Colombian Institute of Culture, now the Ministry of Culture) to write the experimental electronic novel El Primer Vuelo de los Hermanos Wright. 1996-1998, $8K
My current research spans computational mathematics, AI governance, and multi-scale mathematical biology.
AI Governance and Verification: I have established a mathematical impossibility result for zero-error AI (arXiv:2507.06565), which reframes AI reliability as a question of whether failure modes are acceptable and visible. This work underpins a cryptographic audit framework for AI interactions and a multi-agent adjudication algorithm (FOO) for automated truth verification.
Discursive Network Theory: I have developed a mathematical theory of discursive networks that provides a composition protocol for multi-agent AI systems, enabling formal reasoning about how autonomous agents interact, negotiate, and reach consensus.
Data Primitives and Knowledge Representation: We represent heterogeneous and complex data sets of arbitrary size with a reduced set of data primitives: well-defined mathematical objects that serve as typed building blocks for inter-model communication. Our analysis pipelines consume and produce only data primitives, enabling automated knowledge discovery across domains. This work is formalized in the SKED framework.
Adaptive Learning: Training interdisciplinary scientists with heterogeneous backgrounds poses substantial challenges. We have developed an adaptive AI-assisted learning system that minimizes cognitive overhead for individual training and team integration into complex research projects.
Multi-Scale Analysis of Infectious Disease: We study mechanisms connecting multiple scales, from milliseconds through evolutionary time, and from molecular interactions through continental dynamics of infection. This program integrates epidemiological modeling (including asymptomatic carrier dynamics), vector dispersal in heterogeneous landscapes, physiological signal analysis for pre-symptomatic detection, cellular immune interaction modeling, multi-omic data integration (transcriptomics, proteomics, metabolomics, immunomics), and computational drug design via gene regulatory network reconstruction and molecular docking.
COVID-19 Modeling: During the first year of the pandemic, I modeled COVID-19 cases for the City of San Antonio and the South Texas Regional Advisory Council (STRAC). The model was accurate, and received substantial media coverage.