Danny Calegari

Danny Calegari

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

Calegari studied at the University of Melbourne (Bachelor's degree 1994), was then research assistant there, 1996/97 at the 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-Manifold ) . In 2000 he was visiting scholar at the University of California, Davis and Microsoft Research . From 2000 he was Benjamin Peirce Assistant Professor at Harvard University and from 2002 at Caltech as Assistant Professor. From 2003 he was Associate Professor there and from 2006 Professor. Since 2007 he has been Richard Merkin Distinguished Professor there. 2011-12 he was a professor at Cambridge University and since 2012 at the University of Chicago .

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

Ian Agol , Danny Calegari and David Gabai received the 2009 Clay Research Award for the proof of Marden tameness Conjecture ( Zahm Deities presumption of Marden), a conjecture of Albert Marden . 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 then 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. For geometrically finite hyperbolic 3-manifolds it was already proved by Marden and partial results for some geometrically infinite hyperbolic manifolds were also known. From it, among other things (by the work of following William Thurston and Richard Canary ) and a presumption of Lars Ahlfors on the invariant limit quantities small shear groups (namely that they either measure have zero or full measure, in the latter case, the effect of the group is ergodic on the entire edge at infinity ).

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

He is the brother of the mathematician Frank Calegari .

Fonts

• Foliations and the geometry of 3-manifolds . Oxford University Press 2007
• SCL (stable commutator length) . Memoirs Mathematical Society of Japan 2009
• ${\displaystyle \mathbb {R} }$-covered foliations of hyperbolic 3-manifolds . Geom. Topol. 3: 137-153 (1999) 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
• with Walker: Random groups contain surface subgroups. J. Amer. Math. Soc. 28 (2015), no. 2, 383-419.

Web links

• Website at Caltech (English)