Ian Agol

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Ian Agol, Aarhus 2012

Ian Agol (born May 13, 1970 in Hollywood , California ) is an American mathematician who mainly deals with the topology of three-dimensional manifolds .

Agol received his PhD in 1998 from the University of California, San Diego with Michael Freedman ( Topology of hyperbolic 3-manifolds ). He was a professor at the University of Chicago and is an associate professor at the University of California, Berkeley .

Ian Agol, Danny Calegari and David Gabai received the 2009 Clay Research Award for the proof of Marden tameness Conjecture ( " tameness presumption of Marden "), a conjecture of Albert Marden that this however formulated only as a question. It says that a hyperbolic 3-manifold with a finitely generated fundamental group is homeomorphic to the interior of a compact, possibly bounded 3-manifold (the manifold is tame ). An equivalent formulation is that the ends have a local product structure. The conjecture was proven in 2004 by Agol and independently by Calegari and Gabai. Partial results (and especially the validity for geometrically finite hyperbolic 3-manifolds) were already known. Among other things, Agol's doctoral supervisor Freedman had researched it for a long time. From it follows, among other things (through the work of William Thurston and Richard Canary ), a conjecture by Lars Ahlfors about the invariant limit sets of small groups (namely that these have either measure zero or full measure and in the latter case the effect of the group is ergodic in the whole room). The conjecture also completes the classification of Kleinian groups .

In 2005 he was a Guggenheim Fellow . In 2006 he was invited speaker at the International Congress of Mathematicians in Madrid ( Finiteness of arithmetic Kleinian reflection groups ). In 2012 he was awarded the Senior Berwick Prize . For 2013 he was awarded the Oswald Veblen Prize . He is a fellow of the American Mathematical Society . He was selected as plenary speaker at the International Congress of Mathematicians 2014 in Seoul (Virtual properties of 3-manifolds).

In 2012 he proved the “ virtual hook conjecture ”, which goes back to Friedhelm Waldhausen . It says that every irreducible 3 -manifold is finitely overlaid by a hook-manifold . He and Daniel Wise also proved the long open conjecture by William Thurston (1982) that every hyperbolic 3-manifold is virtually fibrillated .

In 2013 he and Daniel Wise received the Oswald Veblen Prize for their fundamental contributions to hyperbolic geometry, 3-dimensional topology and geometric group theory. For 2016 he was awarded the Breakthrough Prize in Mathematics . Also in 2016 he was elected to the National Academy of Sciences .

His twin brother Eric Agol is a professor of astronomy at the University of Washington in Seattle .

Fonts

  • Bounds on exceptional stretch filling , Geom. Topol. 4 (2000), 431-449. ArXiv
  • with D. Long, A. Reid: The Bianchi groups are separable on geometrically finite subgroups , Ann. of Math. (2) 153 (2001), no. 3, 599-621. ArXiv
  • Tameness of hyperbolic 3-manifolds , Preprint 2004. ArXiv
  • with P. Storm, W. Thurston : Lower bounds on volumes of hyperbolic hooks 3-manifolds. With an appendix by Nathan Dunfield, J. Amer. Math. Soc. 20 (2007), no. 4, 1053-1077. ArXiv
  • Criteria for Virtual Fibering , J. Topol. 1 (2008), no. 2, 269-284. ArXiv
  • with D. Groves, JF Manning: Residual finiteness, QCERF and fillings of hyperbolic groups , Geometry and Topology, 13 (2009), no. 2, 1043-1073. ArXiv
  • with Y.Liu: Presentation length and Simon's conjecture , J. Amer. Math. Soc. 25 (2012), no. 1, 151-187. ArXiv
  • The virtual hook conjecture. With an appendix by Ian Agol, Daniel Groves, and Jason Manning, Documenta Math. 18 (2013) 1045-1087 ArXiv
  • with D. Groves, JF Manning: An alternate proof of Wise's malnormal special quotient theorem. Forum Math. Pi 4 (2016), e1, 54 pp

Web links

Commons : Ian Agol  - collection of images, videos and audio files

swell

  1. Stefan Friedl, Thurston's Vision and the Virtual Fibering Theorem for 3-Manifolds, Annual Report DMV, 2014, Issue 4, pdf
  2. Laudation Veblen Prize (PDF; 461 kB)