Talk 1. Janis Lazovskis - 1:00pm
Pure Mathematics Department, University of Waterloo
“The CW-structure and cohomology of the complex Grassmannians””
Using a canonical basis for arbitrary k-spaces, we will construct the Grassmannian of k- subspaces in complex n-space. This will give a very nice description of the cell structure, and also the cohomology of the Grassmannian. A direct limit argument will take this result to k-subspaces of infinite-dimensional complex space. If time permits we will also define the Chern classes directly from the cohomology calcualtions.
Talk 2. Spiro Karigiannis - 2:30pm
Pure Mathematics Department, University of Waterloo
“Metric connections with totally skew torsion: Part I”
Let (M,g) be a Riemannian manifold, and let ∇ be a connection on M which is [i] metric compatible, and [ii] has totally skew-symmetric torsion. We will derive the first and second Bianchi identities, the Ricci identities, and the Bochner-Weitzenb ̈ock formula in this context. The ultimate goal is to find an analogue of the Hodge theorem in this setting.