Proceedings of the National Academy of Sciences of the United States of America

About the PNAS Member Editor
Name Agol, Ian
Location University of California, Berkeley
Primary Field Mathematics
 Election Citation
Agol is a leading researcher in 3-dimensional hyperbolic geometry/topology. His results include the proof that hyperbolic 3-manifolds are geometrically tame, implying that Ahlfors conjecture about limit sets of Kleinian groups is true, and the remarkable fact that every compact hyperbolic 3-manifold is finitely covered by one fibering over the circle.
 Research Interests
Agol's research focusses on 3-dimensional topology, principally the study of hyperbolic 3-manifolds. One main theme is the interaction of topology and geometry, and the study of 2-dimensional surfaces sitting in 3-dimensional spaces. He resolved the tameness conjecture of Marden (and by implication the Ahlfors measure conjecture), which was independently resolved by Danny Calegari and David Gabai. In 2012, he announced the solution of the virtual Haken and virtual fibering conjectures (partly in joint work with Daniel Groves and Jason Manning). The resolution of these conjectures followed from a conjecture of Dani Wise in geometric group theory regarding cube complexes and word-hyperbolic groups (in the sense of Mikhail Gromov), and made extensive use of the techniques of Wise and his collaborators.

 
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