Objectif
"The aim of the proposed research is gaining a better understanding of locally compact groups and their lattices. Our tools are mainly ergodic theoretical.
We propose a variety of novel ideas that open new horizons for research.
The first meta idea is the adoption of tools from the semi-simple theory in order to apply them for general locally compact groups. In particular, we suggest a construction of a ""Weyl group"" and an abstract definition of rank for every locally compact group. We are able to construct a ""Coxeter complex"" and we foresee a construction of a ""building like"" object.
A second set of ideas concerns the category of measure equivalences, which is a natural generalization of the notion of a lattice in a group. This category is long known to be a measurable counterpart of the better studied category of quasi-isometries, yet it misses a good definition of self measure equivalences of an object, analog to the group of quasi-isometries.
We suggest such a definition, and propose to study it, among a variety of related constructions.
A full implementation of our ideas requires a better understanding of locally compact groups.
Thus, an important aspect of the proposed research is that it leaves plenty of room for the study of specific examples and test cases."
Appel à propositions
ERC-2012-StG_20111012
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Régime de financement
ERC-SG - ERC Starting GrantInstitution d’accueil
7610001 Rehovot
Israël