Ian Agol

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

Agol Ph.D. 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 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 conjecture of Marden "), a conjecture of Albert Marden that this, however, formulated only as a question. It states that a hyperbolic 3-manifold with finitely generated fundamental group is homeomorphic to the interior of a compact, possibly bounded 3-manifold (the manifold is tame ). An equivalent formulation is such that the ends have a local product structure. The conjecture was proved in 2004 by Agol and Calegari and Gabai whatever. Partial results (and in particular the validity of geometrically finite hyperbolic 3-manifolds ) were already known. Among other things, Agols Doktorvater Freedman had researched a long time. From it follows, among other things ( by the work of William Thurston and RD Canary ) even a guess by Lars Ahlfors on the invariant limit quantities small shear groups (namely, that they either measure have zero or full measure and in the latter case, the effect of group ergodic throughout the room is ). The assumption completes the classification small shear groups.

2005 he was a Guggenheim Fellow. In 2006 he was invited speaker at the International Congress of Mathematicians in Madrid (Finite Ness of arithmetic Kleinian reflection groups). In 2012 he was awarded the Senior Berwick Prize. For 2013, the Oswald Veblen - Prize was awarded to. He is a Fellow of the American Mathematical Society. He was selected as Plenarsprecher at the International Congress of Mathematicians 2014 in Seoul.

In 2012 he announced a proof of the " virtual hook - guess " indicates a presumption of Friedhelm Waldhausen. It says that every irreducible 3-manifold is finally overlaid by a hook -manifold. In 2013, he shared with Daniel Wise Oswald Veblen - Prize for his fundamental contributions to the hyperbolic geometry, 3 -dimensional topology and geometric group theory.

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

Writings

  • Bounds on exceptional Dehn 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
  • With P.Storm, W. Thurston: Lower bounds on volumes of hyperbolic 3- manifolds hook. 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.
  • With Y.Liu: Presentation length and Simon's conjecture, J. Amer. Math Soc. 25 (2012 ), no 1, 151-187. ArXiv
  • Tameness of hyperbolic 3- manifolds, Preprint 2004. ArXiv
  • The virtual hook conjecture. With an appendix by Ian Agol, Daniel Groves and Jason Manning, Documenta Math 18 (2013) 1045 - 1087 ArXiv
Tameness theorem Oswald Veblen Prize in Geometry Daniel Wise (mathematician)
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