Matthew Beckett, Pure Mathematics, University of Waterloo
"Scaling arguments for the Yang-Mills action"
This talk will introduce the Yang-Mills action on the space of connections as a setting to demonstrate the use of scaling arguments in gaining information about critical points of the energy functional. After giving a general description of the action and the Yang-Mills equations associated to it, I will move on to show how a spatial rescaling in the base space aects the functional. Using arguments related to this rescaling, I will prove an identity which in turn can be used to show the non-existence of some types of solutions to the Yang-Mills equations given certain conditions.
Jordan
Hamilton,
Pure
Mathematics,
University
of
Waterloo
"Generalized Structures on Kodaira Surfaces"
The question of which structures a given surface admits is one asked often in complex geometry. In this talk we will be examining Kodiara surfaces from the point of view of generalized geometry. We will begin with an introduction to generalized geometry, namely generalized complex and Kahler geometry, and then proceed to deform an explicit generalized complex structure on a Kodaira surface. Finally we will prove that none of the generalized complex structures we obtain give rise to a generalized Kahler structure and mention some further results regarding these objects.