Danny Calegari

Danny Calegari Matthew Cornelius ( born May 24, 1972 in Australia ) is an Australian- American mathematician.

Calegari studied at the University of Melbourne ( BA 1994), was there the research assistant, 1996/97 at MSRI and received his doctorate in 2000 at the University of California, Berkeley with William Thurston and Andrew Casson ( Foliations and the Geometry of Three - Manifolds ). In 2000 he was a visiting scientist at the University of California, Davis and at Microsoft Research. From 2000 he was a Benjamin Peirce Assistant Professor at Harvard University and in 2002 at Caltech as an assistant professor. In 2003 he became associate professor there from 2006 professor. Since 2007 he has been there Richard Merkin Distinguished Professor.

Calegari deals with low-dimensional topology, geometry of three-dimensional manifolds and dynamical systems.

Ian Agol, Danny Calegari and David Gabai received the 2009 Clay Research Award for the proof of Marden tameness Conjecture ( Zahm PRIME presumption of Marden ), 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, possibly bounded 3-manifold (the manifold is then tame ). An equivalent formulation is that the ends have a local product structure. The conjecture was proved in 2004 by Agol and Calegari and Gabai whatever. For finite hyperbolic 3-manifolds it has been proved by Marden and partial results for some infinite hyperbolic manifolds were also already known. From it follows, among other things ( by the work of William Thurston and Canary ) even a guess by Lars Ahlfors on the invariant limit quantities small shear groups (namely those either measure have zero or full measure, in the latter case the effect of the group is ergodic throughout the room ).

1999 to 2000 and 2003 to 2005 he was a Sloan Fellow. He is a Fellow of the American Mathematical Society.

Writings

  • Foliations and the geometry of 3 - manifolds. Oxford University Press 2007
  • SCL (Stable commutator length). Memoirs Mathematical Society of Japan 2009
  • -covered foliations of hyperbolic 3- manifolds. Geom Topol. 3 (1999), 137-153 arXiv
  • With Dunfield: Laminations and groups of homeomorphisms of the circle. Invent. Math 152 (2003), no 1, 149-204 ArXiv
  • Promoting essential laminations. Invent. Math 166 (2006), no 3, 583-643 ArXiv
  • With Gabai: shrinkwrapping and the taming of hyperbolic 3- manifolds. J. Amer. Math Soc. 19 (2006 ), no 2, 385-446 ArXiv
  • Stable commutator length is rational in free groups. J. Amer. Math Soc. 22 (2009 ), no 4, 941-961. ArXiv
  • What is stable commutator length? . Notices AMS 2008, PDF file
Mathematical Sciences Research Institute Tameness theorem Sloan Fellows Integrated Authority File
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