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| Richard Canary | |
|---|---|
| Name | Richard Canary |
| Nationality | American |
| Alma mater | Princeton University; University of California, Berkeley |
| Known for | Work in geometric topology, hyperbolic geometry, Teichmüller theory |
| Awards | Oswald Veblen Prize in Geometry |
| Occupation | Mathematician; Professor |
Richard Canary Richard Canary is an American mathematician known for major contributions to geometric topology, hyperbolic geometry, and Teichmüller theory. He has held faculty positions at leading research institutions and has produced influential results linking the theory of Kleinian groups, low-dimensional topology, and dynamics. His work has been recognized by prestigious prizes and has shaped contemporary approaches to deformation spaces and 3-manifold theory.
Canary completed undergraduate studies at Princeton University before pursuing graduate work at the University of California, Berkeley. At Berkeley he studied under advisors active in low-dimensional topology and complex analysis, joining a cohort that included researchers connected to developments around the Thurston hyperbolization theorem and the study of Kleinian groups. His doctoral research positioned him at the intersection of topics related to Riemann surfaces, Teichmüller space, and the deformation theory of discrete groups.
Canary's early appointments included postdoctoral and faculty positions that connected him to research centers such as the Institute for Advanced Study and mathematics departments at major universities. He served on the faculty at institutions with strong programs in topology and geometry, collaborating with colleagues working on the Ending Lamination Conjecture, the theory of geometric structures on 3-manifolds, and the dynamics of group actions on character varieties. Throughout his career he has supervised doctoral students, participated in program committees for conferences organized by the American Mathematical Society and the Mathematical Sciences Research Institute, and contributed survey articles to collections associated with institutions like the National Academy of Sciences and the Royal Society.
Canary's research has produced foundational results in the study of deformation spaces of Kleinian groups and the geometry of hyperbolic 3-manifolds. He has contributed to proofs and refinements related to the Tameness Conjecture and to understanding the topology of hyperbolic 3-manifolds arising from finitely generated Kleinian groups. Canary's work often interrelates techniques from Teichmüller theory, the dynamics of mapping class groups such as the Mapping class group of a surface, and the analytic theory of Riemann surfaces.
Key themes in his contributions include the study of geometric limits, algebraic limits, and the behavior of ending invariants for hyperbolic structures on 3-manifolds. Canary has developed and applied methods for controlling geometric structures via combinatorial and analytic invariants related to laminations, measured foliations, and the geometry of curve complexes. His research helped clarify the relationship between geometric convergence and algebraic convergence for sequences of discrete groups, interacting with major results by figures associated with the resolution of the Ending Lamination Conjecture and the proof of the Ahlfors measure conjecture.
Canary has collaborated with mathematicians working on problems connected to William Thurston’s program for 3-dimensional manifolds, the classification of Kleinian groups by their ending invariants, and the structure of deformation spaces parametrized by Teichmüller spaces and character varieties. His papers often synthesize methods from the work of researchers such as Bers, Minsky, Bonahon, and McMullen.
Canary received recognition for his contributions to geometry and topology, most notably the Oswald Veblen Prize in Geometry for work on hyperbolic 3-manifolds and deformation theory. He has been invited to give lectures at major gatherings such as the International Congress of Mathematicians and plenary or invited sessions at meetings of the American Mathematical Society and the London Mathematical Society. His editorial service includes positions on the boards of journals specializing in low-dimensional topology and geometric structures.
- Canary, R. D.; titles on deformation spaces and limits of Kleinian groups; papers in journals associated with the American Mathematical Society and the London Mathematical Society, addressing questions about algebraic and geometric convergence, ending invariants, and tameness. - Canary, R. D.; collaborations with Minsky, Bonahon, and others on topics connecting Teichmüller theory, curve complex, and hyperbolic geometry; contributions to edited volumes from workshops at institutions such as the Mathematical Sciences Research Institute. - Canary, R. D.; survey articles summarizing developments in the classification of hyperbolic 3-manifolds and the resolution of conjectures originating from Thurston’s program; expository contributions for seminars at Institute for Advanced Study and university lecture series.
Category:American mathematicians Category:Geometers Category:Topologists