Events - June 2022

Talk #1 (9:30am-10:45am): Catalina Quincosis Martínez, Department of Pure Mathematics, University of Waterloo

Spencer Whitehead, Department of Pure Mathematics, University of Waterloo

"Spin and Spinors"

We will define the groups Spin and Pin, the spinor representation, spin structures, and spinor bundles. As time permits we will look at some examples of spin structures and topological obstructions to spinnability. 

MC 5403

Benjamin Anderson-Sackaney, Department of Pure Mathematics, University of Waterloo

"Multipliers on Fourier Algebras"

We will give a brief introduction to multipliers on the Fourier algebra of a locally compact group. Then we will discuss weak amenability, which is a weakening of amenability from the perspective of Leptin's theorem. It was shown by Haagerup that, though free groups are non-amenable, they are weakly amenable. The finale will proceed by outlining a proof of this theorem.

MC 5403

Spencer Whitehead, Department of Pure Mathematics, University of Waterloo

"Introduction to principal bundles"

In this talk we will cover the basic theory of principal bundles and their relation to vector bundles via the frame and associated bundle constructions. We will define connections on principal bundles and structure group reductions, and then if time permits introduce the groups Spin(n) and spin structures on manifolds.

MC 5403

Talk #1 (9:30am - 10:30am): Anton Iliashenko, Department of Pure Mathematics, University of Waterloo

"Some results about Riemannian submersions"

We will go through some results about Riemannian submersions from the Arthur L. Besse's book on Einstein manifolds. For example, we will show that a surjective Riemannian submersion is harmonic iff the fibers are minimal, and some others as the time permits.

Talk #2 (10:45am - 12:15pm): Jean-Pierre Bourguignon, President, European Research Council

Talk #1 (9:30 am - 10:45 am): Amanda Petcu, Department of Pure Mathematics, University of Waterloo

"Introduction to Kahler geometry, part 2"

We will continue with the basics of complex geometry to build the necessary knowledge for studying Kahler geometry. More precisely we will talk about holomorphic forms and vector fields and, certain theorems that relate to integrability of the manifold and almost complex structures.