Talk #1 (1:00-2:30pm)
Ruxandra Moraru, Department of Pure Mathematics, University of Waterloo
"Hitchin pairs on higher-dimensional manifolds"
In this talk, we discuss generalizations of Higgs bundles on curves to higher-dimensional manifolds, consisting of pairs $(E,\phi)$ with $E$ a holomorphic vector bundle on a complex manifold $X$ and $\phi \in H^0(X,End(E) \otimes V)$, where $V$ is a fixed holomorphic vector bundle on $X$. For example, when $V = K_X$, stable pairs $(E,\phi)$ correspond to solutions of the Vafa-Witten equations, and when $V = T^*_X$ (resp. $T_X$), such pairs are called Higgs (resp. co-Higgs) bundles. I will give an overview of some of the known results about Hitchin pairs in higher dimensions and describe some open problems.
Talk #2 (2:30-4:00pm)
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"Formality of compact Kahler manifolds: Episode II"
I will continue the series of talks establishing the formality of compact Kähler manifolds, using a Riemannian geometric approach that could hopefully be adapted to other settings. In this second talk, we will define formality, and then use the del-delbar lemma on compact Kahler manifolds to establish formality. The third talk will likely be about generalizations to other compact Riemannian geometries admitting certain types of parallel differential forms.
MC 5403