Date: 3 October 2014, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: David Johnson, Lehigh University
   Title: Sectional Curvatures

Abstract.  There have been definitions of “higher-order sectional
curvature” for years, but it is curious how those definitions come
about, and how they relate to the truly geometric measurement of the
failure of the parallel postulate in non-Euclidean geometry. They were
also always even-dimensional, since they were based on the
Gauss-Bonnet-Chern theorem. We now have constructed a unified notion of
higher-order sectional curvature, for all dimensions, and show how the
geometric failure of the parallel postulate translates into computable
curvature notions. In the final analysis, however, it is true that all
such curvatures can be defined in terms of ordinary sectional curvature,
so that the classical notion still determines all of these
higher-dimensional versions.