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Leonidas Alaoglu Memorial Lecture
in Mathematics
Monday, April 1, 2013

4:00 p.m.  151 Sloan

Ian Agol
UC Berkeley

The virtual Haken conjecture

Abstract: We will discuss the resolution of the virtual Haken conjecture formulated by Waldhausen in 1968, which states that aspherical 3-dimensional manifolds have a finite-sheeted cover which is Haken, a fortiori which has positive first Betti number. This problem reduces to the case of 3-dimensional hyperbolic manifolds, which is resolved by combining work of Kahn-Markovic and a conjecture of Wise in geometric group theory. We'll give background on these topics, and describe some related conjectures resolved by these techniques.

Ian Agol (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Agol obtained his Ph.D. in 1998 from the University of California, San Diego with Michael Freedman (topology of hyperbolic 3-manifolds). He is a professor at the University of California, Berkeley and a former professor at the University of Illinois at Chicago. Ian Agol, Danny Calegari and David Gabai received the 2009 Clay Research Award 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 is homeomorphic to the interior of a compact 3-manifold. The conjecture was proven in 2004 by Agol, and independently by Calegari with Gabai, and implies the Ahlfors measure conjecture. In 2005 he was a Guggenheim Fellow. In 2012 he became a fellow of the American Mathematical Society. In 2012 he announced a proof of the virtually Haken conjecture. It states that every aspherical 3-manifold is finitely covered by a Haken manifold. In 2013, Agol was awarded the Oswald Veblen Prize in Geometry, along with Daniel Wise. His twin brother, Eric Agol,is an astronomy professor at the University of Washington in Seattle.

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The Leonidas Alaoglu Memorial Lecture was established by friends and family of the late Leonidas Alaoglu in recognition of his great talents, distinguished contributions to mathematics, and long friendship with Caltech. The Institute is privileged to honor his memory with a lecture each year by an outstanding mathematician.

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