Department of Mathematics  
Address: Mathematics
25337

Caltech

Pasadena,
CA 91125
Telephone: (626) 3954335  Fax: (626) 5851728 
Project MATHEMATICS!  Caltech Home 

Leonidas
Alaoglu
Memorial
Lecture 4:00 p.m. 151 Sloan
Ian Agol The virtual Haken conjecture Abstract: We will discuss the resolution of the virtual Haken conjecture formulated by Waldhausen in 1968, which states that aspherical 3dimensional manifolds have a finitesheeted cover which is Haken, a fortiori which has positive first Betti number. This problem reduces to the case of 3dimensional hyperbolic manifolds, which is resolved by combining work of KahnMarkovic 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 threedimensional manifolds. Agol obtained his Ph.D. in 1998 from the University of California, San Diego with Michael Freedman (topology of hyperbolic 3manifolds). 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 3manifold with finitely generated fundamental group is homeomorphic to the interior of a compact 3manifold. 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 3manifold 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.
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. 
