Spring 2014

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

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

Related seminars
also announced.

** Wednesday, January
29th
**

__Speaker:__** Guoliang Yu, Texas A&M University**

__Title____:__**
Finitely embeddable groups, K-theory and non-rigidity of
manifolds** ** **

__Abstract__**:
**In this talk, I will introduce the notion of finitely
embeddable groups to study the degree of non-rigidity for
manifolds.

The class of finitely embeddable groups include all residually
finite groups, amenable groups, hyperbolic groups, linear
groups,

virtually torsion free groups (e.g. Out(F_n)), and any group
of analytic diffeomorphisms. As an intermediate step, I will
explain

how to use group theoretic information to estimate the size of
K-theory. This talk will be accessible to graduate students.

This is joint work with Shmuel Weinberger.

__Speaker:__** Stanley Chang, Wellesley College**

__Title____:__**
Structure sets and virtual structure sets of arithmetic
manifolds** ** **

__Abstract__**:
**This talk will introduce the notion of a structure set in
the context of the surgery exact sequence. We will show that
the

Borel conjecture for compact manifolds cannot be extended into
the proper noncompact setting by exhibiting examples of

arithmetic manifolds whose proper structure set is nontrivial.
At the end we will also introduce the notion of a virtual
structure

set defined on an infinite sequence of covers, and explain
some interesting calculations regarding these objects. The
talk will be

directed towards graduate students who may not be familiar
with surgery theory.

__Speaker:__** Herve Oyono-Oyono, Universite de Metz and CNRS,
France**

__Title____:__**
Persistent Approximation Property for C*-algebras with
propagation** ** **

__Abstract__**:
**The study of elliptic differential operators from the
point of view of index theory and its generalizations to
higher order

indices gives rise to C*-algebras where propagation makes
sense and encodes the underlying large scale geometry.
Prominent

examples for such C*-algebras are Roe algebras, group
C*-algebras and crossed product C*-algebras. Unfortunately,
K-theory

for operator algebras does not keep track of these propagation
properties. Together with G. Yu, we have developed
a quantitative

version of K-theory that takes into account
propagation phenomena. In this lecture we explain that
in many cases, these quantitative

K-theory groups approximate in a particular relevant way the
K-theory. We also discuss connection with the
Baum-Connes and

the Novikov conjecture.

Wednesday, March 26th (SC1312, 3:10-4:00pm)

__Title____:__**
Regularity of canonical operators and the Nebenhulle of
Hartogs domains
**

properties of the Bergman projection operator. We start by reviewing the question of approximating a pseudoconvex domain from

outside by other pseudoconvex domains. Then we present how a curvature type condition on the boundary is sufficient for such

an approximation. At the end, we present new results relating the Bergman projection operator to the rest of the story.

**Tuesday,
April 22nd **

** **

__Speaker:__** Mustafa Kalafat, Michigan State University, and
Tuceli University, Turkey**

__Title____:__**
Self-Dual Metrics on 4-Manifolds** **
**

__Abstract__:
We use hyperbolic 3-manifold geometry to produce 4-manifolds
with special structures. These have locally conformally flat,

self-dual and almost complex structures. We can construct
these 4-manifolds by sketching their Handlebody diagrams.

If time permits, we prove that the connected sum of two
self-dual Riemannian 4-manifolds of positive scalar curvature
is

again self-dual of positive scalar curvature, under a
vanishing hypothesis. The proof involves
Kodaira-Spencer-Freedman deformation

theory and Leray Spectral Sequence. Again if time permits, we
will discuss metrics on the quotients of Enriques Surfaces,
and applications

of the Geometric Invariant Theory, Complex/Almost Complex and
Kahler structures. Some parts are joint work with Selman
Akbulut.

** **

Old Seminar Web-Pages: Fall 2009, Fall
2010