Fall 2013

** Organizers: Gennadi Kasparov, ****Rares
Rasdeaconu****, Ioana Suvaina
**

** Mondays,
4:10-5:00pm in SC 1312 (unless otherwise noted) **

Related seminars
also announced.

** Thursday, September
26th
**

__Speaker:__** Hang Wang, University of Adelaide, Australia**

__Title____:__
**Localized index and
L^2-Lefschetz fixed point formula**

__Abstract__**: **
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).

__Abstract:__**
**The Bach-Maxwell Equations on a 4-dimensional compact
oriented manifold can be thought of as a conformally
invariant version of the classical

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.

classes of the Hilbert schemes of points for a smooth quasi-projective variety of arbitrary pure dimension. The result is based on a geometric construction

of a motivic exponentiation generalizing the notion of motivic power structure, as well as a formula for the generating series of homology characteristic

classes of symmetric products. This is joint work with Cappell, Schuermann, Ohmoto and Yokura.

** **__Abstract:__**
**The talk reports on a frequent appearance of a strategy
that seems to be useful when some sort of "type-III" phenomena
prevent the

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.

Old Seminar Web-Pages: Fall 2009, Fall
2010