Ian Agol

Ian Agol (May 13, 1970 in Hollywood, California) is an American mathematician who deals primarily with the topology of three-dimensional manifolds.^[1]

Agol obtained his Ph.D. in 1998 from the University of California, San Diego with Michael Freedman (topology of hyperbolic 3-manifolds).^[2] He is an associate professor at the University of California, Berkeley^[3] and a former professor at the University of Illinois at Chicago.^[4]

Ian Agol, Danny Calegari and David Gabai received the 2009 a Clay Research Award for the proof of the Marden tameness conjecture, a conjecture of Albert Marden.^[5] 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 that the ends have a local product structure. The conjecture was proven in 2004 by Agol and Calegari and Gabai. Partial results (and in particular the validity of finite hyperbolic 3-manifolds) were already known. The result implies, among other things (by the work of William Thurston and RD Canary), a conjecture of Lars Ahlfors on the invariant limit quantities small shear groups (namely, that they have either measure zero or full measure and have, in the latter case, the effect of the group ergodic in the whole space). The result also completes the classification of small shear groups.^[5]

In 2005 he was a Guggenheim Fellow.^[6]

His twin brother, Eric Agol,^[7][8] is an astronomy professor at the University of Washington in Seattle.^[9]

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