12 September David Lyons, Lebanon Valley College 3 October David Johnson, Lehigh University 7 November Josh Sabloff, Haverford College 5 December Vincent Coll, Lehigh University 6 February Lisa Traynor, Bryn Mawr College 6 March Zhigang Han, Millersville University 10 April Barbara Nimershiem, Franklin and Marshall CollegeTGTS meets at 4:30 p.m. on the first Friday of each month. The public is cordially invited to attend.
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.