School of Mathematics Colloquium

Volumes of hyperbolic 3-manifolds

by Prof. David Gabai (Princeton University, USA)

Monday, July 2, 2012 from to (Asia/Kolkata)
at Colaba Campus ( AG-66 )
Description
As part of his revolutionary work on hyperbolic geometry in
the 1970's, Thurston generalizing work of Jorgensen and Gromov, showed that the set of volumes of complete finite volume hyperbolic 3-manifolds is closed and well ordered. Recently,  Robert Meyerhoff and Peter Milley and the speaker showed that the Weeks manifold is the unique lowest volume
closed orientable one, culminating a 30+ year effort by many mathematicians using a wide variety of geometric and topological techniques.  This lecture will survey these and other developments and discuss some of the many open problems in the area.