Ian Agol (born May 13, 1970) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

who deals primarily with the

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

of three-dimensional manifolds.

Education and career

Agol graduated with B.S. in mathematics from the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

in 1992 and obtained his Ph.D. in 1998 from the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...

. At UCSD, his advisor was

Michael Freedman Michael Hartley Freedman (born April 21, 1951) is an American 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 4-dimensional gen ...

and his thesis was ''Topology of Hyperbolic 3-Manifolds''. He is a professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

and a former professor at the

University of Illinois at Chicago The University of Illinois Chicago (UIC) is a Public university, public research university in Chicago, Illinois. Its campus is in the Near West Side, Chicago, Near West Side community area, adjacent to the Chicago Loop. The second campus esta ...

Contributions

In 2004, Agol proved the

Marden tameness conjecture Marden may refer to: Places Australia * Marden, South Australia, a suburb of Adelaide England * Marden, Herefordshire * Marden, Kent ** Marden Airfield ** Marden railway station * Marden, Tyne and Wear * Marden, West Sussex ** East Marden ** N ...

, a conjecture of

Albert Marden Albert Marden (born 18 November 1934) is an American mathematician, specializing in complex analysis and hyperbolic geometry. Education and career Marden received his PhD in 1962 from Harvard University with thesis advisor Lars Ahlfors. Marden h ...

. It states that a hyperbolic 3-manifold with finitely generated

fundamental group In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of ...

homeomorphic In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphi ...

to the interior of a

compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...

3-manifold. The conjecture was also independently proven by

Danny Calegari Danny Matthew Cornelius Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory. Educ ...

and

David Gabai David Gabai is an American mathematician and the Hughes-Rogers Professor of Mathematics at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects. Biography David Ga ...

, and implies the

Ahlfors measure conjecture In mathematics, the Ahlfors conjecture, now a theorem, states that the limit set of a finitely-generated Kleinian group is either the whole Riemann sphere, or has measure 0. The conjecture was introduced by , who proved it in the case that the Kl ...

. In 2012 he announced a proof of the

virtually Haken conjecture In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is ''virtually Haken''. That is, it has a finite cover (a covering s ...

, which was published a year later. The conjecture (now theorem) states that every aspherical 3-manifold is finitely covered by a

Haken manifold In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which ...

. In 2022 he posted on the

ArXiv arXiv (pronounced "archive"—the X represents the Greek letter chi ⟨χ⟩) is an open-access repository of electronic preprints and postprints (known as e-prints) approved for posting after moderation, but not peer review. It consists of ...

a proof of Cameron Gordon's 1981 conjecture on

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

saying that ribbon concordance forms a partial ordering on the set of knots.

Awards and honors

Agol, Calegari, and Gabai received the 2009

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

for their proof of the Marden tameness conjecture. In 2005, Agol was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2013, Agol was awarded the

Oswald Veblen Prize in Geometry __NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was founded in 1961 in memory of Oswald Veblen. The Veblen Prize is now worth US$5000, and is ...

, along with Daniel Wise. In 2015, he was awarded the 2016

Breakthrough Prize in Mathematics The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013. It is funded by Yuri Milner and Mark Zuckerberg and others. The annual award comes with a cash gift of $3 million. The Breakthrough Prize ...

, "for spectacular contributions to

low dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theor ...

and

geometric group theory Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such group (mathematics), groups and topology, topological and geometry, geometric pro ...

, including work on the solutions of the

tameness A tame animal is an animal that is relatively tolerant of human presence. Tameness may arise naturally (as in the case, for example, of island tameness) or due to the deliberate, human-directed process of training an animal against its initially ...

, virtually Haken and virtual fibering conjectures." In 2016 he was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

Personal

His identical twin brother,

Eric Agol Eric Agol (born May 13, 1970 in Hollywood, California ) is an American astronomer and astrophysicist who was awarded a Guggenheim Fellowship in 2017. Career Agol is a professor and astrophysicist at the University of Washington in the Departmen ...

, is an astronomy professor at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...

Seattle Seattle ( ) is a seaport city on the West Coast of the United States. It is the seat of King County, Washington. With a 2020 population of 737,015, it is the largest city in both the state of Washington and the Pacific Northwest regio ...

References

External links

* {{DEFAULTSORT:Agol, Ian 20th-century American mathematicians 21st-century American mathematicians Topologists University of California, San Diego alumni University of Illinois Chicago faculty University of California, Berkeley College of Letters and Science faculty Living people 1970 births Clay Research Award recipients Fellows of the American Mathematical Society Members of the United States National Academy of Sciences People from Hollywood, Los Angeles Mathematicians from California American identical twins