Organizers: Bruce Hughes and Mark Sapir

Wednesdays, 4:10pm in SC 1424 (unless otherwise noted)

• Date: 2 February 2005
  • Speaker: Mark Sapir, Vanderbilt University
  • Title:  Hilbert space compression of Thompson group and other diagram groups
  • Abstract:
    This is a joint work with Goulnara Arzhantseva and Victor Guba.
    The Hilbert space compression of a metric space X is the supremum of all
    a < 1 such that there exists a uniform embedding   f : X --> H (a Hilbert
    space) such that     n^a < dist(f(x),f(y)) < Cn     for all sufficiently large n
    and all  x, y in X with  dist(x,y) < n. By Guentner and Kaminker, Hilbert space
    compression > 1/2 implies Guoliang Yu's property A.
    We find the first examples of finitely generated groups with Hilbert space
    compression not 0 or 1. Namely, we show that the Hilbert space compression
    of the R.Thompson group F is exactly 1/2, and the
    Hilbert space compression of the wreath product Z wr Z is between 1/2 and
    3/4. Some open problems will be also discussed.

• Date: 9 February 2005
  • Speaker: Alexey Muranov, Vanderbilt University
  • Title: On Virtual Polycyclicity of Torsion-free Groups with Finite Regular File Bases
  • Abstract:
    The following question asked by V. V. Bludov in the Kourovka notebook in
    1995 is answered in this paper:
    If a torsion-free group  G  has a finite system of generators  a_1, ..., a_n
    such that every element of  G  has a unique presentation in the form
    a_1^{k_1}\ldots a_n^{k_n},  where  k_i \in \Bbb Z,
    is it true that  G  is virtually polycyclic?
    The answer is negative.
    A counterexample is constructed by means of a group presentation
    by generators and defining relations.

• Date: 16 February 2005
  • Speaker: Ashot Minasyan, Vanderbilt University
  • Title:  Separable Subsets of Negatively Curved Groups
  • Abstract:
    A word hyperbolic group  G  is called QERF if every quasiconvex subgroup is
    equal to an intersection of finite index
    subgroups. We show that in any such group, the product of finitely many
    quasiconvex subgroups is closed in the profinite
    topology on  G.  This is a generalization of a result of  L. Ribes and
    P. Zalesskii concerning products of finitely generated subgroups in a
    free group.

   

• Date: 23 February 2005
  • Speaker: John Ratcliffe, Vanderbilt University
  • Title: On the isomorphism problem for finitely generated Coxeter groups. I, Basic Matching
  • Abstract:
    A base of a Coxeter system $(W,S)$ is a noncyclic spherical subgroup of maximal rank,
    that is, a finite subgroup of the form $\langle A\rangle$, with $A\subset S$, $|A| > 1$, and $|A|$ as large as possible.
    If $(W,S')$ is another Coxeter system for the same Coxeter group $W$, we prove that each base of $(W,S)$ matches a unique base of $(W,S')$. 
    We completely analyze when the matching bases are not isomorphic.

   

• Date: 2 March 2005
  • Speaker: Graham Niblo, Southampton
  • Title: Geometry and analysis applied to CAT(0) cube complexes
  • Abstract:
    We show how to use the family of normal cube paths in a
    finite dimensional CAT(0) cube complex to  define a family of large
    scale Lipschitz embeddings of the cube complex into a Hilbert space,
    and  compute the asymptotic compression of these maps. This is joint
    work with Sarah Campbell.

• Date: 3 March 2005 Thursday, Department of Mathematics Colloquium
  • Speaker: Graham Niblo, Southampton
  • Title: Property T from a geometric group theorist's point of view
  • Abstract: Kazhdan's property T (which concerns the unitary representation theory of a locally compact group) has a geometric interpretation for countable discrete groups. We will describe this interpretation and explore it in the context of groups acting on CAT(0) cubical complexes.

   

• Date: 14 March 2005 Monday
  • Speaker: Michah Sageev, Technion and the University of Utah
  • Title: CAT(0) cubical complexes in group theory
  • Abstract:
    We will discuss CAT(0) cubical complexes and their connection
    with various topics in geometric group theory.

     

• Date: 15 March 2005 Tuesday, joint with NCGOA Seminar, SC1432
  • Speaker: John Crisp, Dijon
  • Title: Quasi-isometric embeddings in the pure braid group
  • Abstract:
    In this joint work with Bert Wiest (Rennes) we develop a technique for
    embedding groups quasi-isometrically in a pure braid group, as well as in
    the group of area preserving diffeomorphisms of the 2-disk (with a suitable
    metric). I shall describe how this can be done for a large class of
    right-angled Artin groups. This result can then be used to exhibit
    quasi-isometric embeddings of a variety of hyperbolic groups in both the
    braid group and the group of area preserving diffeomorphisms of the disk.

• Date: 30 March 2005
  • Speaker: Yuri Bahturin, Memorial University (Canada) and Moscow University (Russia)
  • Title: Group Graded Simple Algebras
  • Abstract:
    This talk is based on a  recent joint work with S. Sehgal and M. Zaicev. The main result of this paper gives a complete descriprion of finite-dimensional associative algebras which are graded by an arbitrary group and have no nonzero proper graded ideals.

   

• Date: 5 - 8, 11 - 15 April  2005, Special Lecture Series;
  Tuesday, April 5 in SC 1307 from 3:00 to 5:00; Wednesday, April 6 and Wednesday, April 13 in SC1308; other days in SC 1307. MWF from 4:00 to 5:00; TR from 3:00 to 4:00.
  • Speakers: Alain Connes (Collège de France, IHES & Vanderbilt) and Matilde Marcolli (Max-Planck Institute Bonn)
  • Title: Noncommutative geometry: from Quantum Physics to Motives
  • Note: The first lecture will be an overview on Tuesday, April 5, from 3:00 to 5:00 in SC 1432.

• Date: 20 April 2005
  • No meeting