Bogdan Gavrea
Assistant Professor
School of Mathematical and Natural Sciences
Arizona State University
Biography
I earned my Ph.D. in Applied Mathematics from the University of Maryland, Baltimore County in 2006, focusing on the simulation of rigid-body systems with applications in robotics. After completing my doctoral studies, I held a postdoctoral appointment at the GRASP Lab, University of Pennsylvania. In 2007, I began my faculty career at the Technical University of Cluj-Napoca, Romania, where I was active for nearly fourteen years. Before joining Arizona State University, I also worked briefly in the private sector as a Consultant and Analytic Scientist. I am currently an Assistant Professor of Applied Mathematics in the School of Mathematical and Natural Sciences at Arizona State University.
Degrees Earned
PhD/Applied Mathematics/2006 MS (Advanced Study Degree)/Applied Mathematics/2001 BS/Mathematics/2000
Research Areas
Applied Mathematics; Machine Learning/AI; Mathematics
Research Interests
Research Interests: - Differential complementarity systems; - Applied Math methods in machine learning and AI; - Mathematical inequalities (applications in probability, statistical learning and approximation theory); - Planning and control of robotic systems - Numerical and stochastic optimization
Topical Areas
Applied Mathematics; Artificial Intelligence and Intelligent Systems; Mechanical Engineering; Statistics and Probability
Research Synergy
My research focuses on differential complementarity problems, applied mathematical methods in machine learning and AI, stochastic optimization, mathematical inequalities with applications in probability and approximation theory, and the planning and control of robotic systems. Within Applied Mathematics, my work contributes to the theoretical development of complementarity systems and to numerical methods for the simulation of rigid-body dynamics. In relationship to Statistics and Probability, I study mathematical inequalities with applications to probability theory, statistical learning, and approximation theory, developing analytical tools to assess generalization and uncertainty in data-driven models. In Artificial Intelligence, my research aims to bridge mathematical modeling and learning by developing optimization-based techniques that enhance the reliability, interpretability, and control of AI systems. One emerging direction involves applying mathematical tools from robot safe navigation to the large language model (LLM) setting, exploring how formal models of safety can inform the behavior of intelligent systems. The connection to Mechanical Engineering arises naturally through the planning and control of robotic systems, as well as through the design of complementarity-based numerical schemes for the simulation of rigid-body systems. Together, these lines of inquiry define an interdisciplinary research approach uniting mathematical theory, control theory, computational methods, and intelligent system design.
Motivation
My motivation for participating in the Sustainable Research Pathways (SRP) Program comes from its strong alignment with my research focus, mentorship philosophy, and commitment to building new and productive research collaborations. The SRP framework offers a unique opportunity to work with laboratory researchers and scientists across disciplines, which represents a major incentive for my participation. Equally important, the program provides a valuable platform for the students on my team to engage in state-of-the-art research within a collaborative and interdisciplinary environment. Through SRP, I aim to introduce my students to the lab research ecosystem and help them strengthen their technical, analytical, and collaborative skills. I believe that a research partnership initiated through this program can serve as the foundation for long-term collaboration and joint publications at the intersection of applied mathematics, engineering sciences, and AI/machine learning.
Supervising Students Plan
My approach emphasizes active mentorship aimed at helping students become self-directed researchers and practitioners capable of bridging mathematical theory with real-world applications. In terms of skill development, I will encourage students to gain experience in applied mathematical modeling and analysis, scientific writing and presentation, and collaborative research practices. The team’s research plan will include regular internal meetings and collaborations with researchers from the participating labs and projects, ensuring consistent communication and progress. My role as a mentor will be to guide students in defining and refining their research direction, helping them stay on the right path and optimize their efforts toward meaningful and measurable outcomes in a strongly collaborative setting. Since both students in my team are master’s students, an additional focus of my mentorship will be to support them through the dissemination process, aiming for a joint publication involving the students, myself, and our lab or project collaborators.
Student Merit
I met both Haran and Teja recently through a research idea I advertised to students in robotics. We began discussing a topic of shared interest — extending control theory techniques used in robotics for safe navigation to safe chain-of-thought reasoning in the context of large language models (LLMs). One promising direction we identified is the use of Control Barrier Functions within the chain-of-thought (CoT) process to enforce CoT safety. Both students demonstrated a strong interest in bridging their robotics background with emerging developments in AI through a structured mathematical perspective. They are motivated, curious, and eager to engage with established researchers across related fields. Haran has a solid background in control theory and is a member of the IRIS Lab at ASU. The work conducted in the IRIS Lab — particularly on contact-rich manipulation and the design of control and optimization methods for safe autonomous systems, aligns closely with my own research expertise. Teja is another excellent student who is enthusiastic about connecting AI methodologies with classical robotics principles. He has a solid foundation in applied mathematics, has participated in AI hackathons, and has contributed to several AI–robotics coding projects, demonstrating both initiative and technical versatility. In summary, both students possess the aptitude, motivation, and collaborative spirit necessary for this program. I am confident that their participation will not only strengthen our project’s interdisciplinary focus but also provide them with valuable exposure and professional growth within the broader research community.
Lightning Talk Title
Robot Safe Navigation Techniques in Large Language Models
Keywords
numerical optimization; differential complementarity problems; large language models; control barrier functions; rigid body systems