He has been a researcher at CINVESTAV's Department of Mathematics since June 1994, where he conducts research in Topology, Geometry, Algebra, and Homotopy Theory, applying these fields in Robotics and Big Data Analysis. Jesús has supervised 32 theses (11 at the doctoral level, 14 at the master's level, and 7 at the bachelor's level) and is currently supervising one doctoral and one master's thesis. He has published over 50 original research articles in prestigious international journals and has participated in more than 120 congresses and conferences in his specialty, where he has been a plenary speaker in 10 of them.

with a thesis on "Synchronization in Distributed Networks," which introduced the unison problem. Following this, he pursued postdoctoral studies at the Massachusetts Institute of Technology under Nancy Lynch from 1993 to 1995, where his research contributed to three main topics: developing a method for computing achievable clock synchronization precision based on communication and individual clock drift bounds, creating a simulation for direct translations of algorithms and impossibility results from one model to another, and studying the deep connection between distributed computing and algebraic topology. Since 1994, Rajsbaum has collaborated with Maurice Herlihy, leading to a research project spanning over 30 years, culminating in the book "Distributed Computing Through Combinatorial Topology," co-authored with mathematician Dmitry Feichtner-Kozlov. This topological perspective has expanded beyond distributed computing, leading to work in combinatorial topology, directed topology, and connections with logic, runtime verification, and social choice theory.