## UNIVERSITY OF PENNSYLVANIA

## Department of Mathematics

Spring 2009 -Hans Rademacher Lectures in Mathematics

David Gabai

## Department of Mathematics

Princeton University

will speak on

## 3-dimensional hyperbolic geometry, taut foliations, knot theory and the topology of ending lamination space

Abstract: We outline a proof that the Weeks manifold is the lowest volume closed orientable hyperbolic 3-manifold. Along the way we discuss a number of beautiful and simple ideas needed to understand the topology and geometry of low dimensional manifolds. Topology vs. Geometry: The Hunt for the smallest closed hyperbolic 3-manifold

Monday....April 20, 2009.....4:30pm...A6 DRL

Abstract: We address the general question of when does a Thurston norm minimizing surface in a 3-manifold with multiple torus boundary components remain norm minimizing under Dehn filling, e.g. when does a minimal genus Seifert surface for an oriented link in the 3-sphere remain minimal genus after Dehn surgery on a component of the link. Foliations and surgery on links in S^{3}

Tuesday....April 21, 2009....4:30pm...A6 DRL

Almost filling laminations and the connectivity of ending lamination space: Proof of the Storm Conjecture I

Wednesday.....April 22, 2009....4:30pm...A8 DRL

Almost filling laminations and the connectivity of ending lamination space: Proof of the Storm Conjecture II

Thursday.....April 23, 2009....4:00pm...4C8 DRLAbstract: We will show that if the hyperbolic surface S is not the 3 or 4 holed sphere or one holed torus, then the space of ending laminations (i.e. those with each leaf dense and "fill up" S) is path connected, locally path connected and cyclic. In 2001 Peter Storm conjectured that this space was connected.

List of Previous Rademacher Lecturers Lectures will be held in the David Rittenhouse Laboratory,

S.E. corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: 4E17 DRL at 4:00pm.For further information, please call the Department of Mathematics at the University of Pennsylvania (215) 898-8627.