Eugene Lerman

Eugene Lerman is a Professor in the Department of Mathematics at the University of Illinois Urbana-Champaign (UIUC). He holds a primary appointment in the Department of Mathematics within the College of Liberal Arts & Sciences. His research focuses on advanced geometric and topological structures with applications to dynamical systems and mathematical physics.

Research interests include Hamiltonian systems with symmetry, singular reduction, contact toric manifolds, orbifolds, Lie 2-groups and algebras, coupled cell networks, hybrid dynamical systems, differential spaces, and C∞-ringed spaces. He has contributed to foundational work in geometric analysis and categorical approaches to differential geometry.

Recent publications (2020–2024) explore topics like Cartan calculus on C∞-ringed spaces, vector fields on subcartesian spaces, and stability analysis of symmetric tops. His work bridges abstract algebraic structures with concrete dynamical systems, emphasizing symmetry principles across scales.

Lerman is affiliated with the Department of Mathematics at UIUC and maintains an active research website: http://lerman.web.illinois.edu/.