Noncommutative Geometry Research Group

The Noncommutative Geometry Group focuses on the generalization of results, tools, and constructions from both differential geometry and algebraic geometry to the noncommutative setting. Using methods primarily from category theory and homological algebra, this has led to developments on the noncommutative analogues of jets, differential operators, higher order connections, quantization, Spencer cohomology, de Rham cohomology, and diffeomorphisms. The group also investigates new phenomena which appear only in the noncommutative setting, novel insights into the classical setting which arise when viewed from a noncommutative perspective, and applications of the general theory to problems in mathematical physics.