Benoit Charbonneau & Ren Zhu, Pure Mathematics, University of Waterloo
Ren Zhu
“Introduction to Cˇech Cohomology”
Cohomology is a widespread notion in mathematics which comes in many different forms. One starts with an object X and defines groups of cocycles and coboundaries on X, and the cohomology group is the quotient of cocycles by coboundaries. These cohomology groups contain valuable information and also give us a useful tool since many concepts can be defined or interpreted in terms of cohomology. In this talk I will focus on Cˇech cohomology for a sheaf F on a Riemann surface X. I will define and discuss the groups H0(X,F) and H1(X,F). As an application we will see that H1(X, O∗) parametrizes the isomorphism classes of line bundles on X.
Benoit Charbonneau
will speak on
“Flow of connections, Part II”
We will explore other aspects of the Yang-Mills flow in the set of connections compatible with a given holomorphic structure on a vector bundle.