Organizers: Gennadi Kasparov, Rares
Rasdeaconu, Ioana Suvaina
4:10-5:00pm in SC 1312 (unless otherwise noted)
Speaker: Hang Wang, University of Adelaide, Australia
Title: Localized index and L^2-Lefschetz fixed point formula
In this talk , we introduce a class of localized indices for
the Dirac type operators on a complete Riemannian manifold,
where a discrete group acts properly,
co-compactly and isometrically. These localized indices, generalizing the $L^2$-index of Atiyah, are obtained by taking certain traces of the higher index for the Dirac type
operators along conjugacy classes of the discrete group. Applying the local index technique, we also obtain an $L^2$-version of the Lefschetz fixed point formula for
orbifolds. These cohomological formulae for the localized indices give rise to a class of refined topological invariants for the quotient orbifold. The talk is related to the joint
work with Bai-Ling Wang (ArXiv 1307.2088).
Monday, October 7th, (will
start at 4:05pm)
Einstein-Maxwell Equations in general relativity. Riemannian metrics which solve the BM equations have interesting geometric properties. In this talk,
I will introduce these equations and give several variational characterizations. I will also show that extremal Kahler metrics are among the solutions and
discuss their role in this variational setting.
Monday, October 28th
The talk reports on a frequent appearance of a strategy
that seems to be useful when some sort of "type-III" phenomena
existence of certain invariant structures for dynamical systems in analysis, topology and geometry. The approach is called "reduction to type
II", and usually involves some extension of the dynamical system in such a natural way that the resulting system is large enough to carry the desired
invariant structure. Our examples will demonstrate that - in search for such extensions - one naturally needs to involve (or to develop) some very
important techniques relevant to the context.