Talk 1. Emilio Verdugo Paredes - 1:00pm
Pure Mathematics Department, University of Waterloo
“Construction of Vector Bundles on the Complex Tori using Factors of Automorphy”
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.
Talk 2. Mateusz Olechnowicz - 2:30pm
Pure Mathematics Department, University of Waterloo
“Elliptic functions and the Weierstrass ℘ function”
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.