/ School of Mathematics
Geometry, Mathematical Analysis, Topology
Michael Kapovich works on geometry and geometric group theory. His main contributions have been to the theory of discrete subgroups of Lie groups, quasiisometric rigidity, geometric structures on manifolds (such as hyperbolic structures, flat conformal structures, complex and real projective structures), character varieties of finitely generated groups and the theory of mechanical devices. His work connects to algebraic geometry, geometric representation theory, metric geometry, symplectic geometry and Riemannian geometry. Examples of such connections are analogues of Mumford's GIT in the context of discrete groups, application of the theory of mechanical devices and polyhedral complexes to the topology of complex algebraic varieties, applications of the theory of polygons in symmetric paces and Euclidean buildings to the problem of tensor product decomposition of irreducible representations of semisimple Lie groups.