## 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, June 18, 2014 — 1:00 PM EDT

E is an extension of M by P if there is a short exact sequence 0 → M → E → P → 0. If these are modules then E/M ≃ P; if these are (holomorphic) vector bundles then locally this is a split extension, but of course globally the extension can be more complicated. Goal of the talk: see how these extensions correspond to certain cohomology classes.

Let M be a compact complex manifold. The famous Hodge Theorem states that the Dol- beault cohomology groups of M are finite dimensional and gives a very useful L2 orthogonal decomposition for the forms on M. Using the Hodge Theorem one can prove beautiful results such as Serre Duality, the Hodge decomposition for Khler manifolds, the Hard Lefschetz Theorem etc. In a series of talks we will discuss the Hodge Theorem and go over some of these results. In this first talk we will describe various notions from Linear Algebra such as adjointness, extending inner products to the exterior algebra etc. We will also introduce all the operators and the cohomology groups involved in the Hodge Theorem. Time permitting we will start to talk about the Fourier analysis involved in the proof of the Hodge Theorem.

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 centralized within our Office of Indigenous Relations.