COARSE GEOMETRY WORKSHOP
12th January (Monday) 2004 -- 16th January (Friday) 2004
At Department of Mathematics, Kyoto University
Organizers: Kenji Fukaya, Tsuyoshi Kato
Gregory C. Bell (Pennsylvania State University) Pennsylvania
Title 1: Intorduction to asymptotic dimension
In this first talk I will introduce various notions of asymptotic
dimension and other closely related asymptotic invariants.
Title 2: Asymptotic dimension and group actions
In this talk I will discuss ways that one can recover the asymptotic
dimension of a group from its action on a metric space. This yields upper
bound estimates on dimension for large classes of groups.
Fujiwara Koji (Tohoku University) Sendai
Title: CAT(0) dimensions of discrete groups
Ishiwata Satoshi (Tohoku University) Sendai
Title: Geometric and analytic properties in the behavior
of the random walks on nilpotent covering graphs
Kamimura Shingo (Keio University) Hiyoshi
Title: Discrete Quantum Groups
Moriyoshi Hitoshi (Keio University) Hiyoshi
Title 1: A twisted \Gamma index thoerm
Title 2: A manifold with end like Cantor set and UHF algebras
Ohta Shin-ichi (Kyoto University) Kyoto
Title: Regularity of harmonic functions on metric spaces
Yann Ollivier (Paris Universite) Orsay
Title: Overview of results on random groups
We will present the philosophy and main results about random
groups: critical density and phase transitions phenomenon,
algebraic and spectral properties, and construction of groups with
prescribed Cayley graphs.
Michah Sageev (Technion) Haifa
Title 1: CAT(0) cubical complexes in group theory
We will give an overview of groups acting on CAT(0) cubical complexes
and discuss how they relate to various other topics in geometric group
Title 2: Maximally symmetric trees
We will discuss a quasi-isometric rigidity result
for group actions onbounded valence bushy trees.
We then discuss how this result,
together with some results on edge-indexed graphs,
can be used to characterize the ``best" model
geometries for the class of virtually free groups.
This is joint work with Lee Mosher and Kevin Whyte.
Qin Wang (Dong Hua University) Shanghai
Title: Ideal Structure of Uniform Roe Algebras of Coarse Spaces
Daniel Wise (McGill University) Montreal
Title 1: On the vanishing of the 2nd L^2 betti number.
I will discuss conditions on a 2-complex which guarantee that its 2nd
L^2 betti number vanishes. One application is that the fundamental group of
2-complexes are "coherent" which means all their finitely generated
subgroups are finitely presented.
Title 2: Cubulating Small Cancellation Groups.
I prove that groups satisfying certain small-cancellation conditions act
properly discontinuously and cocompactly on CAT(0) cube complexes. In
particular, my results hold for finitely presented groups with
presentations satisfying either the C'(1/4)-T(4) or the C'(1/6) conditions.
These results can be viewed as a "geometrization theorem" for
small-cancellation group. I will discuss codimension-1 subgroups, relations
to Kazhdan's property-T, and the dichotomy between word-hyperbolicity and
ZxZ subgroups for certain small-cancellation groups. The results depend
upon an elegant but powerful method for constructing actions on cube
complexes that was introduced by Sageev.
Nick Wright (Vanderbilt University) Nashville
Title 1: Coarse geometry and $C^*$-algebras
In this first talk I will introduce the Roe algebra, and discuss
how this encodes information about the large scale structure of a space. I
will also talk about the relation with the K-homology of a space.
Title 2: $C_0$ coarse geometry and scalar curvature
In this second talk I will discuss the $C_0$ variant of coarse
geometry, and I will indicate how coarse geometry can be used to establish
upper bounds on the scalar curvature content of a space.
Yamashita Yasushi (Nara Women University) Nara
Makoto Tamura (Osaka Sangyo University) Osaka
Yoshiyuki Nakagawa (Ryukoku University) Kyoto
Title: On Gersten's problem
Andrzej Zuk (Chicago University, ENS Lyon) Chicago, Lyon
Title: On the Cheeger constant for modular surfaces