## 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 11, 2014 — 1:00 PM EDT

We will discuss the concept of sheaves of functions on manifolds and the related definitions, as well as the notion of an exact sequence of sheaves. After some basic examples, the process of going from a short exact sequence of sheaves to a long exact sequence on sheaf cohomology will be described, as well as the effect of the boundary map defining the first Chern class of a complex line bundle. This foreign differential geometric terminology will be meticulously defined in an algebraic geometry setting.

Picking up where we left off, we will determine the differential equation for ℘ and use it to show that to each lattice we may assign an elliptic curve parametrized by elliptic functions. The converse of this assignment is known as the inversion problem for Eisenstein series. Its solution, given by the uniformization theorem, is the goal of our talk. Our main tools will be the modular group and the j-invariant.

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.