IAN AGOL – Wikipedia

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Ian Aga (* May 13, 1970 in Hollywood, California) is an American mathematician who is primarily concerned with the topology of three-dimensional diversity.

Agol received his doctorate in 1998 at 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 Associate Professor an der University of California, Berkeley.

Ian Agol, Danny Calegari and David Gabai received the Clay Research Award for the evidence of the Marden Tameness Conjecture (“Membership of the Meve”), a presumption of Albert Mardi, which he only formulated as a question. It states that a hyperbolic 3 manigle with finally generated fundamental group Homeomorph is the interior of a compact, possibly born 3-mannibleness (the manifold is tame ). An equivalent wording is that the ends have a local product structure. The assumption was proven in 2004 by Agol and regardless of Calegari and Gabai. Partial results (and in particular the validity for geometrically finite hyperbolic 3-manniblige) were already known. Among other things, Agols Doctor Freedman had also researched it for a long time. From it, among other things, (through the work of William Thurston and Richard Canary) also follows a presumption of Lars Ahlfors about the invariant border quantities of small groups (namely that they have either level or full and in the latter case the effect of the group ergodic is in the whole room). The presumption also completes the classification of small groups.

In 2005 he was Guggenheim Fellow . In 2006 he was Invited Speaker At the international mathematician congress in Madrid ( Finiteness of arithmetic Kleinian reflection groups ). In 2012 he was awarded the Senior Berwick Prize. The Oswald Veblen Prize was awarded for 2013. He is Fellow of the American Mathematical Society. He was selected as a plenary spokesman at the 2014 International Mathematician Congress in Seoul (Virtual Properties of 3-Manifolds).

In 2012 he demonstrated the “virtual-hook presumption” back to Friedhelm Waldhausen. It states that every Ireduzible 3-mannibligality is finally overlaid by a hook man-dibleness. With Daniel Wise, he also demonstrated the long open assumption of William Thurston (1982) that every hyperbolic 3-mannibleness is virtually fitted. [first]

In 2013, together with Daniel Wise, he received the Oswald veblen price for his fundamental contributions to hyperbolic geometry, 3-dimensional topology and geometric group theory. [2] The Breakthrough Prize in Mathematics was awarded for 2016. He was also elected to the National Academy of Sciences in 2016.

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

  • Bounds on exceptional Dehn filling , Geom. Topol. 4 (2000), 431–449. ArXiv
  • mit 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
  • mit P. Storm, W. Thurston: Lower bounds on volumes of hyperbolic Haken 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
  • mit D. Groves, J. F. 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 Haken conjecture. With an appendix by Ian Agol, Daniel Groves, and Jason Manning, Documenta Math. 18 (2013) 1045–1087 ArXiv
  • mit D. Groves, J. F. Manning: An alternate proof of Wise’s malnormal special quotient theorem. Forum Math. Pi 4 (2016), e1, 54 pp
  1. ↑ Stefan Friedl, Thurston’s Vision and the Virtual Fibering Theorem for 3-Manifolds, Annual Report DMV, 2014, Issue 4, pdf ( Memento of the Originals from February 8, 2016 in Internet Archive ) Info: The archive link has been used automatically and not yet checked. Please check original and archive link according to the instructions and then remove this note. @first @2 Template: Webachiv/Iabot/www.uni-regensburg.de
  2. ↑ Laudatio Veblen Prize (PDF; 461 kB)