Alejandro Cabrera, Distinguished Researcher (Beatriz Galindo Senior) in the Department of Mathematics since 2026

Alejandro Cabrera is a mathematician working in differential geometry, mathematical physics, and their applications. He holds a B.Sc. and a Master’s degree in theoretical physics from Instituto Balseiro (Argentina), and a Ph.D. in mathematics from Universidad Nacional de La Plata (Argentina). He has held postdoctoral positions at IMPA (Brazil) and the University of Toronto (Canada). Since 2011, he has been affiliated with the Universidade Federal do Rio de Janeiro (Brazil), where he served first as an Adjunct and later as an Associate Professor, and has been a Full Professor since 2022. He is currently a Distinguished Researcher (Beatriz Galindo Senior) in the Department of Mathematics at the Universitat Politècnica de Catalunya starting in 2026.

Alejandro Cabrera has made diverse contributions to the broad area of Poisson geometry and related branches of mathematical physics, addressing both theoretically oriented questions and establishing concrete applications and connections between different areas. Among these contributions, we highlight: the establishment of novel and precise relations between Kontsevich’s formal quantization and a Lie-theoretic quantization program based on symplectic groupoids; the provision of complete Lie-theoretic characterizations of groupoid operations and general geometric structures; the reduction of infinite-dimensional geometries arising in gauge theory and topological field theories; the development of links between dynamical systems and singular spaces (differentiable stacks); and the formulation of geometric solutions to concrete mechanical problems involving rotating bodies and optimization in robotic motion. One of the applications was used in the context of twisting somersaults in the 2016 Olympics [link to El País article].

His current research interests also include integrability and analytical aspects of non-formal quantization, the study of higher Lie theory, and Lie-theoretic methods in numerical integration.