Talk #1 (1:00pm - 2:30pm)
Michael Albanese, Department of Pure Mathematics, University of Waterloo
"The Schoen-Yau Stable Minimal Hypersurface Technique"
In the quest to determine whether tori admit metrics of positive scalar curvature, two powerful techniques were developed: enlargeability due to Gromov and Lawson, and the stable minimal hypersurface technique due to Schoen and Yau. Having previously discussed the former, we will introduce the latter. In particular, we will show that if a closed smooth manifold admits a positive scalar curvature metric, then so does any stable minimal hypersurface.
Talk #2 (2:30pm - 4:00pm)
Lucia Martin Merchan, Department of Pure Mathematics, University of Waterloo
"Geometry of calibrated submanifolds"
Given a Riemmanian manifold M endowed with calibration α, the condition that a submanifold L of M is calibrated is a first order condition. By contrast, its geometric data, given by the second fundamental form A and the induced tangent and normal connections ∇ on TL and D on NL, respectively, is second order information. In this talk, we characterize the conditions imposed on the geometric data (A,∇,D) when a submanifold L is calibrated with respect to a calibration α on M which is parallel. After that, we apply our results to some interesting calibrated geometries, such as Kähler, Calabi-Yau, G_2 and Spin(7) manifolds.
MC 5403