Graduate School of Mathematics, Nagoya University
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Research - Past Conferences and Workshops - Geometry and Groups

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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)
10:30–11:30Nicolas Monod
(Univ. of Geneva)
CAT0 spaces, splitting and superrigidity (1)
13:30–14:30Nicolas MonodCAT0 spaces, splitting and superrigidity (2)
15:00–16:00Toshiyuki Akita
(Hokkaido Univ.)
Cohomological aspects of Coxeter groups
July 4 (Tue)
10:30–11:30Nicolas MonodCAT0 spaces, splitting and superrigidity (3)
13:30–14:30Koji Fujiwara
(Tohoku Univ.)
Asymptotic geometry of curve graphs
15:00–16:00Takefumi Kondo
(Kyoto Univ.)
Fixed-point property for CAT(0) spaces
July 5 (Wed)
10:30–11:30Nicolas MonodCAT0 spaces, splitting and superrigidity (4)
July 6 (Thu)
10:30–11:30Nicolas MonodCAT0 spaces, splitting and superrigidity (5)
13:30–14:30Narutaka Ozawa
(Univ. of Tokyo)
Amenable actions and applications (1)
15:00–16:00Narutaka OzawaAmenable actions and applications (2)
July 7 (Fri)
10:30–11:30Nicolas MonodCAT0 spaces, splitting and superrigidity (6)
13:30–14:30Taro 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.