Mathematical Research at FSU

Low dimensional and geometric topology

Low dimensional topology is the study of topological manifolds of dimensions two, three and four, and includes the study of knots and links, mapping classes, and a variety of classification problems. William Thurston brought attention to the delicate interplay between geometric and topological structures in low-dimensions, and founded the field of geometric topology.

A discrete conformal tiling of the plane.

At FSU, Wolfgang Heil and Sergio Fenley work on classifications of 3-manifolds from different viewpoints. Heil looks at constructions of 3-manifolds from simpler pieces, while Fenley, a former student of Thurston, investigates foliations, laminations and flows. Kathleen Petersen works on character varieties of 3-manifolds, incorporating algebraic geometry and number theory into the study of manifolds, Phil Bowers works in conformal geometry and tilings of the plane. Sam Ballas works in geometric structures on manifolds and their interactions with representation theory and dynamics.

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