August 26
Stanley Chang (Wellesley College)
Bounded rigidity of manifolds and asymptotic dimension growth
September 2
no talk
September 9
Romain Tessera (Vanderbilt University)
The stable Borel conjecture for linear groups
Inspired by the notion of asymptotic dimension, we will introduce a more flexible large-scale geometric property of a group called Finite Decomposition Complexity. This property will be proved for a large class of groups such as all subgroups of GL_n(A) where A is a commutative ring. On the other hand, this property being shaped for "cutting and pasting" methods, we show that if a group has Finite Decomposition Complexity, then it satisfies the Novikov and the stable Borel conjecture.
September 16
[Joint Group Theory & Topology - Noncommutative Geometry Seminar]
Christophe Pittet (University of Marseille)
Bounded 2-cocycles on Lie groups
Characteristic numbers of flat principal bundles admit universal bounds if the structural group is algebraic. This was first discovered by Milnor for SL(2,R) then generalized by Gromov and others to all algebraic groups. We show that the algebraic condition can be weakened. This is joint work with Chatterji, Mislin, Saloff- Coste.
September 23
Mrinal Raghupathi (Vanderbilt University)
Constrained Nevanlinna-Pick Interpolation
Given points $z_1,\ldots,z_n, w_1,\ldots,w_n$ in the unit disk, the Nevanlinna-Pick theorem gives a characterization for the existence of a holomorphic map $f$ that maps the disk to the disk and "interpolates" $z_i$ to $w_i$. Problems of this type are usually called Nevanlinna-Pick problems. In this talk I will provide some background and describe the classical setting. I will then look at a simple variation on the original problem that arises from studying the interpolation problem for curves embedded in the bidisk. If time permits I will talk about the interpolation problem on Riemann surfaces.
(Some of the results presented here were obtained in joint work with Ken Davidson, Vern Paulsen and Dinesh Singh).
September 30
Jesse Peterson (Vanderbilt University)
A remark on Popa's HT factors
If $\Gamma$ is a discrete group with the Haagerup property and $\Gamma$ acts freely and ergodically on a standard probability space $(X, \mu)$, then Popa showed that $L^\infty(X, \mu)$ is the only possible rigid Cartan subalgebra of $N = L^\infty(X, \mu) \rtimes \Gamma$. We will explain these results and some consequences using derivations on the von Neumann algebra $N$. This setting will allow us to generalize Popa's result to include a larger class of groups, e.g. groups with positive first $\ell^2$-Betti number.
October 7
Bogdan Nica (Vanderbilt University)
Group actions on median spaces
I will start with a mini-survey of bounded vs. proper group actions. Then I will talk about the relation between bounded/proper actions on median spaces, and bounded/proper actions on Hilbert spaces.
October 14
Guoliang Yu (Vanderbilt University)
An equivariant index theorem and its applications
I will discuss an equivariant index theorem for the Dirac operator on noncompact manifolds and its applications to geometry and topology of three dimensional manifolds. This is joint work with Stanley Chang and Shmuel Weinberger. The talk should be accessible to general audience including graduate students.
October 21
no talk
October 28
Dan Ramras (Vanderbilt University)
An introduction to Quillen's algebraic K-theory
In the early 70's, Quillen discovered a topological construction which unified the lower algebraic K-groups defined by Grothendieck (K_0), Whitehead (K_1), and Milnor (K_2) and produced a notion of higher algebraic K-theory. I'll describe Quillen's approach to higher K-theory for rings. In particular, I'll describe his Q-construction, and I'll explain why it gives the correct definition of K_0, the group of formal differences between projective modules. I'll also describe some of the theorems Quillen proved using this approach. This will be an introductory talk, and I will try to keep the formal nonsense to a minimum.
November 4
Dan Ramras (Vanderbilt University)
An introduction to Quillen's algebraic K-theory II
After reviewing the Q-construction, I'll explain the proof that it yields the correct notion of K_0. We'll then discuss the relationship between the Q-construction and Quillen's second approach to K-theory, the plus construction. Time permitting, I'll say a little bit about how negative K-groups can be brought into the picture. This relies on the theory of bounded modules, developed by Pederson and Weibel.
November 11
Yves de Cornulier (Rennes)
On asymptotic cones of polycyclic groups
I'll give an example of a polycyclic group whose asymptotic cones have abelian and non-trivial fundamental group. (joint with R. Tessera).
November 18
Ziga Virk (University of Tennessee - Knoxville)
Realizations of Countable Groups as Fundamental Groups of Compacta
We prove that every countable group can be realized as the fundamental group of a path connected compact subspace of four-dimensional Euclidean space. According to theorem of Shelah such space can not be locally path connected if the group is not finitely generated. This constructions complements realization of groups in the context of compact Hausdorff spaces, that was studied by Keesling, Rudyak and Przezdziecki.
November 25
no talk
December 2
no talk
December 9
Jan Spakula (Universität Münster)
On controlled coarse homology
We study a coarse homology theory with prescribed growth conditions on the growth of cycles' coefficients. For a finitely generated group G with the word length metric this homology theory turns out to be related to amenability of G. We characterize vanishing of a fundamental class in our homology in terms of an isoperimetric inequality on G and explain that on any group at most linear control is needed for this class to vanish.
As applications, we show connections to isodiametric profiles, existence of primitives of the volume form with prescribed growth and obstructions to weighted Poincare inequalities.
This is joint work with Piotr Nowak.
December 16
Erik Guentner (University of Hawaii)
Coarse geometry, permanence and cube complexes
January 13
Rongwei Yang (SUNY Albany)
Projective spectrum in Banach algebras
For an element a in a unital algebra B over the complex field C, its classical spectrum is the collection of complex numbers z such that a-ze is not invertible. This spectrum can be viewed as a numerical measurement of the interplay between a and the unit e. Sometimes it is necessary to consider interplays among n elements, say a_1, ..., a_n, and a rather natural generalization of the classical spectrum is the notion of projective spectrum of (a_1, ..., a_n) which is the collection of points in C^n such that z_1a_1+z_2a_2+...+z_na_n is not invertible. In this talk we will look at some geometric and topological properties of projective spectrum. The talk is self-contained and accessible to graduate students.
January 20
Guoliang Yu (Vanderbilt University)
Operator norm localization and its applications to K-theory
January 27
Hervé Oyono Oyono (Universite Blaise Pascal, and CNRS)
On principal noncommutative torus bundles
Principal noncommutative torus bundles form a class of continuous fields of non-commutative tori that generalises principal torus bundles. They show up as local form of the "missing T-dual" in string theory. As we shall see, these bundles are quite irregular in any topological sense. We introduce K-theoretical invariants for principal noncommutative torus bundles in order to discuss their classification. This is joint work with S. Echterhoff and R. Nest.
February 3
Xiang Tang (Washington University)
Relative index of CR structures
We discuss a new proof of the Atiyah-Weinstein conjecture on the index of Fourier integral operators and the relative index of CR structures. This talk is based on a recent joint work with Boutet de Monvel, Leichtnam, and Weinstein.
February 10
John Roe (Penn State)
Second quantizing the 'Roe algebra'?
A video of Mike Freedman talking at MSRI last fall ("Towards Quantum Characteristic Classes", available at
http://www.msri.org/communications/vmath/VMathVideos/VideoInfo/3895/show_video) relates some familiar (to me!) concepts in large scale index theory with ideas coming from solid state physics and quantum computing. I will try to offer some exegesis of this video and the new mathematical explorations that it suggests.
February 17
Rufus Willett (Penn State)
Index theory for operators with slowly oscillating coefficients
The talk is motivated by a concrete question from operator theory: in coarse geometric language, it asks for an index formula for Fredholm operators in the uniform Roe algebra of Z^n. We will describe a solution in the special case that the operators have 'slowly oscillating' (or 'Higson') coefficients. Looking at more general discrete groups, we will also briefly discuss connections of our approach with the Baum-Connes conjecture via the stable Higson corona of Emerson and Meyer.
February 24
no talk
March 3
no talk
March 10
Yves de Cornulier (Rennes)
Metabelian groups in the space of finitely generated groups
In the space of finitely generated (marked) groups, we study the topology at the neighbourhood of finitely presented metabelian groups.
March 24
Xiang Fang (Kansas State University)
Some Commutative Algebraic Methods in Multivariable Operator Theory
I will present a few examples of commutative algebraic techniques applied to Hilbert space operators, with the aim to illustrate the principle that "commutative algebraic methods are useful for the 'local study' of operators". In particular, I will talk about Samuel multiplicity, Fredholm index, and I-adic analysis for operators. The long term goal is to provide new techniques in order to foster the development of multivariable operator theory.
March 31
Bobby Ramsey (IUPUI)
The isocohomological property, higher Dehn functions, and relatively hyperbolic groups
The property that the polynomial cohomology, with coefficients, of a finitely generated discrete group is isomorphic to the group cohomology is called the (weak) isocohomological property for the group. This property first appears in the work of Connes and Moscovici on the Novikov conjecture for hyperbolic groups. In the case when the group is of type $F_\infty$, i.e. it has a classifying space the type of a simplicial complex with finitely many cells in each dimension, we show that the isocohomological property is equivalent to the classifying space satisfying polynomially bounded higher Dehn functions. If the group is hyperbolic relative to a collection of subgroups, each of which is of type $F_\infty$ and isocohomological, we show that the group itself has these properties.
April 7
Carla Farsi (University of Colorado at Boulder)
Orbifold $\Gamma$-sectors
In this talk I will introduce the $\Gamma$-sectors of a general orbifold, where $\Gamma$ is a finitely generated group. This construction generalizes several other constructions in the literature for orbifolds that are quotients of manifolds by the action of finite groups. I will give several applications of $\Gamma$-sectors to the study of orbifolds. This is joint work with C. Seaton.
Upcoming
April 14
Piotr Nowak (Texas A&M)
Isoperimetric inequalities and controlled coarse homology
We will discuss a controlled coarse homology theory and its connection to isoperimetric inequalities on discrete spaces. This connection is manifested by vanishing of a certain fundamental class in the 0-dimensional homology group. We will also discuss the homological Burnside theorem and present applications to e.g. primitives of differential forms.
(This talk will complement the talk given by Jan Spakula earlier in this seminar, however I will not assume any familiarity with that talk)
