معرفی
Augustin-Liviu Mare is a Professor in the Department of Mathematics and Statistics within the Faculty of Science at the University of Regina, Canada, where he has maintained an active research profile since joining as an Assistant Professor in 2004. His academic career spans multiple institutions including the University of Toronto, McMaster University, and Babes-Bolyai University in Romania, reflecting deep international engagement in geometric research.
Mare earned his Ph.D. from the University of Augsburg (1998) under Jost-Hinrich Eschenburg with the dissertation "Topology of Isotropy Orbits." His educational trajectory demonstrates foundational training in geometric topology that directly informs his current research.
His research centers on the geometry and topology of differentiable manifolds, with specialized focus on Lie groups, Riemannian symmetric spaces, and flag manifolds. Mare investigates how symmetry properties expressed through group actions impact manifold structure, bridging pure geometry with theoretical physics concepts like the Toda lattice. His work spans topological classification to precise Riemannian and symplectic structures, with significant contributions to equivariant and quantum cohomology theories.
Analysis of his 15 most recent publications reveals consistent exploration of connectivity properties in moment maps and Schur-Horn maps, equivariant cohomology of group actions (particularly cohomogeneity-one and hyperpolar), and quantum deformations of cohomology rings. These works demonstrate an evolving trajectory toward deeper connections between convexity theorems, integrable systems, and topological invariants in symmetric spaces.
While no specific awards are documented in available sources, Mare's sustained publication record in elite journals including Mathematische Zeitschrift and Documenta Mathematica indicates significant scholarly recognition. His collaborative network features prominent mathematicians like Oliver Goertsches and Chen He, underscoring his position within international research communities.
Mare maintains active research collaborations but no dedicated laboratory structure is indicated. His work environment centers on theoretical investigations through mathematical collaboration, with recent publications suggesting continued exploration of Schur-Horn map properties and their extensions to broader geometric contexts.
