## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, July 9, 2014 1:00 PM EDT

Pure Mathematics Department, University of Waterloo

The Mordell-Weil theorem says that if $E$ is an elliptic curve over $\mathbf{Q}$, then the abelian group $E(\mathbf{Q})$ is finitely generated. Mazur's theorem then pinpoints the torsion part of $E(\mathbf{Q})$ as one of fifteen finite groups. Central to Mazur's proof is the notion of a group scheme, which is a group object in a category of schemes. In this talk we will define group objects and give examples in various categories. We will also discuss affine groups and see how they can be realized as group schemes."

Pure Mathematics Department, University of Waterloo

In this final talk we will discuss some applications of the Hodge Theorem. The main application will be the Hodge decomposition for compact Kahler manifolds. A hermitian manifold is said to be Kahler if the associated (1,1) form is d-closed. It turns out that this condition is enough to relate the various operators corresponding to d,\partial, \bar(\partial) together. This will then enable us to simplify a lot of relations obtained by the Hodge Theorem. We will give examples of Kahler manifolds, prove the Hodge decomposition and use it to discuss the structure of Kahler manifolds.

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 x43484

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within our Office of Indigenous Relations.