Agenda der Universität Bern im neuen Erscheinungsbild

Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern
Philosophischnaturwissenschaftliche Fakultät
Departement Mathematik und Statistik
Mathematisches Institut
Mathematical Colloquia
Monday, 17 October 2016
17:15 h, Lecture Room B 78
Prof. Dr. Masato Mimura, Tohoku University / EPFL
Bounded and unbounded generation; and
fixed point properties
Fix a complete metric space. We say that a finitely generated group has the fixed point property
(f.p.p.) relative to it if every isometric action admits a global fixed point. A surprising theorem of
Kazhdan implies that SL(n,Z), the special linear group over the ring of integers, has f.p.p. relative to
Euclidean spaces, and even to Hilbert spaces (that is, infinite dimensional Euclidean spaces),
provided that n is at least 3.
One influential way to show that f.p.p. was invented by Y. Shalom [Publ. IHES, 1999]. It employs
so-called "Bounded Generation" (BG) of a group by finite family of subgroups. This method is
completely powerful as long as BG is available. However, in general, BG condition is too strong to
In this talk, I will present a recent resolution to the barrier of the case where BG is invalid/unknown.
In this talk, I will give the definition of BG; exhibit some examples; and explain why this was
essential in previous works. Finally, I will describe our new approach to f.p.p., that is free from
exploiting BG.
Sekretariat, Mathematisches Institut, Sidlerstrasse 5, CH-3012 Bern, Tel. +41 (0)31 631 88 21, Fax +41 (0)31 631 85 10
[email protected],