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Ian Agol [needs IPA ] (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds .[2]
Education and career [ edit ]
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 .[3] He is a professor at the University of California, Berkeley [4] and a former professor at the University of Illinois at Chicago .[5]
Contributions [ edit ]
In 2004, Agol proved the Marden tameness conjecture , a conjecture of Albert Marden .[6] 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 .[6]
In 2012, he announced a proof of the virtually Haken conjecture , which was published a year later.[7] 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.[8] [9]
Awards and honors [ edit ]
Agol, Calegari, and Gabai received the 2009 Clay Research Award for their proof of the Marden tameness conjecture.[6]
In 2005, Agol was a Guggenheim Fellow .[10] In 2012 he became a fellow of the American Mathematical Society .[11]
In 2013, Agol was awarded the Oswald Veblen Prize in Geometry , along with Daniel Wise .[12]
In 2015, he was awarded the 2016 Breakthrough Prize in Mathematics , "for spectacular contributions to low dimensional topology and geometric group theory , including work on the solutions of the tameness , virtually Haken and virtual fibering conjectures."[13]
In 2016, he was elected to the National Academy of Sciences .[14]
Personal [ edit ]
His identical twin brother, Eric Agol ,[15] [16] [17] is an astronomy professor at the University of Washington in Seattle .[18]
References [ edit ]
^ Mackenzie, Dana; Cipra, Barry (December 20, 2006). What's happening in the mathematical sciences . American Mathematical Society . pp. 15–16. ISBN 978-0-8218-3585-2 .
^ Ian Agol at the Mathematics Genealogy Project .
^ "Ian Agol" . University of California, Berkeley Department of Mathematics. Retrieved June 25, 2011 .
^ "Ian Agol" . University of Illinois at Chicago . Archived from the original on June 16, 2011. Retrieved June 25, 2011 .
^ a b c "Clay Research Award" . Clay Mathematics Institute . Archived from the original on June 26, 2011. Retrieved June 25, 2011 .
^ Agol, Ian (2013). "The virtual Haken conjecture. With an appendix by Agol, Daniel Groves, and Jason Manning" (PDF) . Documenta Mathematica . 18 : 1045–1087. doi :10.4171/dm/421 . MR 3104553 . S2CID 255586740 .
^ Sloman, Leila (2022-05-18). "How Complex Is a Knot? New Proof Reveals Ranking System That Works" . Quanta Magazine . Retrieved 2022-05-20 .
^ Agol, Ian (2022-01-10). "Ribbon concordance of knots is a partial order". arXiv :2201.03626 [math ].
^ "Ian Agol – Guggenheim Fellows Finder" . John Simon Guggenheim Memorial Foundation . Archived from the original on September 21, 2012. Retrieved June 25, 2011 .
^ List of Fellows of the American Mathematical Society , retrieved 2012-11-03.
^ Joint Mathematics Meetings Prize Booklet: January 2013 Prizes and Awards: Oswald Veblen Prize in Geometry, pp. 14–18
^ "Breakthrough Prizes Give Top Scientists the Rock Star Treatment" . New York Times . Nov 8, 2015.
^ National Academy of Sciences Members and Foreign Associates Elected , News from the National Academy of Sciences, National Academy of Sciences , May 3, 2016, archived from the original on May 6, 2016, retrieved 2016-05-14 .
^ "Interview with Ian Agol" (PDF) . Notices of the American Mathematical Society . 63 (1 ): 24. January 2016.
^ "Obituaries – Alan Agol" . Visalia Times-Delta . October 4, 2005. p. C2.
^ "Alan Agol" . Marin Independent Journal . October 5, 2005.
^ "Eric Agol" . University of Washington Department of Astronomy. Retrieved June 25, 2011 .
External links [ edit ]
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