12th January (Monday) 2004 -- 16th January (Friday) 2004

At Department of Mathematics, Kyoto University

Organizers: Kenji Fukaya, Tsuyoshi Kato

Monday Tuesday Wednesday Thursday Friday
10:00-11:00 Wang Sageev Fujiwara Wright Ishiwata
11:30-12:30 Bell Wise Zuk Moriyoshi Oliivier
14:30-15:30 Sageev Wright Free Ohta Bell
16:00-17:00 Yamashita Kamimura Wise Moriyoshi


  • 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 theory.

    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 certain 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