## 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

Wednesday, May 21, 2014 — 1:00 PM EDT

Pure Mathematics Department, University of Waterloo

The goal of this talk will be to demonstrate the construction of vector bundles on the complex tori using a quotient defined with factors of automorphy. The definition of the complex tori uses a complex lattice, which allows very natural projection maps from the trivial vector bundle on Cn. By relaxing conditions on the factor of automorphy, we can later generate non-holomorphic vector bundles, which can be identified using characteristic classes.

Pure Mathematics Department, University of Waterloo

The set of periods Ω(f) of a non-constant meromorphic function f is a free abelian subgroup of (C, +). Its rank is either 0, 1, or 2; in the latter case, Ω(f ) is called a lattice and f is called elliptic. We will first prove some nice properties of elliptic functions, and then prove that they actually exist. After introducing Weierstrass’s ℘ function, we will show that the field of elliptic functions is generated by ℘ and ℘′. Time permitting, we will obtain the transcendental parametrization of an elliptic curve and show how the group law on the cubic is nothing more than addition in C.

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