
ADDRESS: Furocho, Chikusaku, Nagoya, Japan / POSTAL CODE: 464-8602

Research Past Conferences and Workshops Geometry and Groups

Update: 2006/08/07

Research

Mini-Workshop “Geometry and Groups”

Date: July 3–7, 2006
Place: Rm 333, Hotel North-Inn Sapporo, Hokunoukenpokaikan
Kita-shijoh 7–1, Chuoh-ku, Sapporo
Organizers: Masahiko Kanai (Nagoya Univ.), Shin Nayatani (Nagoya Univ.), Hiroyasu Izeki (Tohoku Univ.)

Program

July 3 (Mon)
10:30–11:30	Nicolas Monod (Univ. of Geneva)	CAT0 spaces, splitting and superrigidity (1)
13:30–14:30	Nicolas Monod	CAT0 spaces, splitting and superrigidity (2)
15:00–16:00	Toshiyuki Akita (Hokkaido Univ.)	Cohomological aspects of Coxeter groups
July 4 (Tue)
10:30–11:30	Nicolas Monod	CAT0 spaces, splitting and superrigidity (3)
13:30–14:30	Koji Fujiwara (Tohoku Univ.)	Asymptotic geometry of curve graphs
15:00–16:00	Takefumi Kondo (Kyoto Univ.)	Fixed-point property for CAT(0) spaces
July 5 (Wed)
10:30–11:30	Nicolas Monod	CAT0 spaces, splitting and superrigidity (4)
July 6 (Thu)
10:30–11:30	Nicolas Monod	CAT0 spaces, splitting and superrigidity (5)
13:30–14:30	Narutaka Ozawa (Univ. of Tokyo)	Amenable actions and applications (1)
15:00–16:00	Narutaka Ozawa	Amenable actions and applications (2)
July 7 (Fri)
10:30–11:30	Nicolas Monod	CAT0 spaces, splitting and superrigidity (6)
13:30–14:30	Taro Yoshino (RIMS)	Existence problem of a compact Clifford–Klein form and tangential homogeneous spaces

Abstract of lectures by Prof. Monod

The lectures will begin as an introduction to cat(0) spaces, also called Hadamard spaces. These spaces are defined by imposing a simple inequality on triangles in completely general metric spaces in order to imitate the notion of "non-positive sectional curvature" familiar in Riemannian geometry. That level of generality allows to produce relatively simple arguments that are interesting even for the special case of Riemannian manifolds.

We will introduce from the very beginning some of the general techniques in cat(0) geometry. Our guiding goals will be (1) to prove a splitting theorem in the spirit of Lawson-Yau and Gromoll-Wolf; (2) to prove a superrigidity theorem in the spirit of Margulis. This goals will provide motivation for the general theory.