Alejandro Bravo-Doddoli

I am a mathematician working in sub-Riemannian geometry, geometric mechanics, and geometric control theory.

My research focuses on the geometry and dynamics of sub-Riemannian geodesics, particularly the classification of globally minimizing geodesics, also called metric lines. One of my main contributions is the development of the sequence method, a geometric technique for proving global minimality without explicitly integrating the geodesic equations.

I am also interested in the integrability of Hamiltonian systems and the dynamics of nonholonomic mechanical systems. My research explores connections between differential geometry, optimal control, and dynamical systems, including the integrability of sub-Riemannian geodesic flows and nonholonomic billiards.

I received my Ph.D. in Mathematics from the University of California, Santa Cruz, under the supervision of Professor Richard Montgomery. I am currently a Visiting Professor at the University of Michigan and will begin a three-year postdoctoral position at the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico, in January 2027. Previously, I was a Postdoctoral Assistant Professor at the University of Michigan, where I worked with Professor Anthony Bloch.

I have over twelve years of experience teaching mathematics at the university level. In 2025, I received the B. Alan Taylor Outstanding Postdoctoral Assistant Professor Teaching Award from the University of Michigan.

I am also committed to undergraduate research mentorship. At the University of Michigan, I served as director of the Laboratory of Geometry at Michigan (LoG(M)), where I coordinated undergraduate research projects and mentored students in mathematical research and communication.

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