Introduction to metric and comparison geometry

Series: 
Geometry Topology Working Seminar
Friday, February 13, 2009 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
School of Mathematics, Georgia Tech
Organizer: 
Comparison geometry studies Riemannian manifolds with a given curvature bound.  This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the first (2 hour) lecture I shall explain what volume comparison is and derive several applications.