Master's Thesis Talk

Aidan Patterson, Department of Pure Mathematics, University of Waterloo

"Para-Holomorphic Algebroids and Para-Complex Connections"

The goal of this talk is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost para-complex structure, and use this to define a notion of para-holomorphic algebroid. We investigate connections on para-holomorphic algebroids and determine an appropriate sense in which they can be para-complex. Finally, we show through a series of examples how the theory of exact para-holomorphic algebroids with a para-complex connection is a generalization of both para-Kähler geometry and the theory of Poisson-Lie groups.

Zoom link:

• https://us02web.zoom.us/j/85946115595?pwd=OWt5eTU4YTJPSUJ2dWFOOURrZ1QrQT09

• Meeting ID: 859 4611 5595

• Passcode: 290377