Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                             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.

             Tuesday, February 25th

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.



             Tuesday, March 11th

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)

                  Speaker: Yunus Zeytuncu, University of Michgan-Dearborn

Title: Regularity of canonical operators and the Nebenhulle of Hartogs domains
Abstract: In this talk, we discuss the relation between the geometric properties of the boundary of a domain in C^n and the analytic
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, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013