## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, May 13, 2014 — 1:00 PM EDT

Pure Mathematics Department, University of Waterloo

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.

Pure Mathematics Department, University of Waterloo

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.

Location

MC - Mathematics & Computer Building

4062

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1