My research focuses on developing the mathematical foundations for safe and reliable autonomous systems. We work at the intersection of control theory, dynamical systems, optimization, and machine learning, with a particular emphasis on developing rigorous guarantees for learning-enabled systems.
As autonomous systems become increasingly capable and widespread, fundamental questions remain about how to ensure they behave safely, reliably, and predictably. My group develops new theory and algorithms aimed at providing provable safety and performance guarantees for complex decision-making systems.
I am particularly interested in working with students who enjoy mathematics and are excited by challenging, open-ended research problems. Strong preparation in areas such as applied mathematics, control theory, optimization, dynamical systems, or machine learning is highly desirable.
This position is best suited for students who are motivated by developing new theory and contributing to fundamental advances rather than applying existing methods. Research often involves tackling problems for which no solution is known, and successful students are typically those who are intellectually curious, persistent, and excited by difficult questions.
Prospective students interested in pursuing a Ph.D. are welcome to contact me directly (cdanielson@unm.edu). Please include a brief description of your background, research interests, and relevant coursework or research experience.
