Ian Agol
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Through Topology
Education and career
Agol graduated with B.S. in mathematics from the California Institute of Technology in 1992 and obtained his Ph.D. in 1998 from the University of California, San Diego. At UCSD, his advisor was Michael Freedman and his thesis was Topology of Hyperbolic 3-Manifolds. He is a professor at the University of California, Berkeley and a former professor at the University of Illinois at Chicago.
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Contributions
In 2004, Agol proved the Marden tameness conjecture, a conjecture of Albert Marden. It states that a hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3-manifold. The conjecture was also independently proven by Danny Calegari and David Gabai, and implies the Ahlfors measure conjecture.
In 2012, he announced a proof of the virtually Haken conjecture, which was published a year later. The conjecture (now theorem) states that every aspherical 3-manifold is finitely covered by a Haken manifold.
In 2022, he posted on the ArXiv a proof of Cameron Gordon's 1981 conjecture on knot theory saying that ribbon concordance forms a partial ordering on the set of knots.
Personal
His identical twin brother, Eric Agol, is an astronomy professor at the University of Washington in Seattle.