Ian Agol is an American mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 who deals primarily with the topology

Topology

Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

 of three-dimensional manifold

Manifold

In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....

s.

Agol obtained his Ph.D. in 1998 from the University of California, San Diego with Michael Freedman

Michael Freedman

Michael Hartley Freedman is a mathematician at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the Poincaré conjecture. Freedman and Robion Kirby showed that an exotic R4 manifold exists.Freedman was born...

 (topology of hyperbolic 3-manifolds). He is an associate professor at the University of California, Berkeley

University of California, Berkeley

The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

 and a former professor at the University of Illinois at Chicago

University of Illinois at Chicago

The University of Illinois at Chicago, or UIC, is a state-funded public research university located in Chicago, Illinois, United States. Its campus is in the Near West Side community area, near the Chicago Loop...

.

Ian Agol, Danny Calegari

Danny Calegari

Danny M. C. Calegari is the Richard Merkin Professor of Mathematics at the California Institute of Technology, and is one of the recipients of the 2009 Clay Research Award for his work in geometric topology and geometric group theory....

 and David Gabai

David Gabai

David Gabai, a mathematician, is currently a professor at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects....

 received the 2009 a Clay Research Award

Clay Research Award

The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...

 for the proof of the Marden tameness conjecture, a conjecture of Albert Marden. It states that a hyperbolic 3-manifold with finitely generated fundamental group

Fundamental group

In mathematics, more specifically algebraic topology, the fundamental group is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other...

 is homeomorphic to the interior of a compact

Compact space

In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...

, 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-manifold

Hyperbolic 3-manifold

A hyperbolic 3-manifold is a 3-manifold equipped with a complete Riemannian metric of constant sectional curvature -1. In other words, it is the quotient of three-dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely and properly discontinuously...

s) were already known. The result implies, among other things (by the work of William Thurston

William Thurston

William Paul Thurston is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds...

 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.

In 2005 he was a Guggenheim Fellow

Guggenheim Fellowship

Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...

.

His twin brother, Eric Agol, is an astronomy professor at the University of Washington

University of Washington

University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...

 in Seattle.