Concept

Théorie géométrique des groupes

Publications associées (44)

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Fixed points and amenability in non-positive curvature

Nicolas Monod

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...

Springer2013

Counting Sheaves Using Spherical Codes

Philippe Michel

Using the Riemann Hypothesis over finite fields and bounds for the size of spherical codes, we give explicit upper bounds, of polynomial size with respect to the size of the field, for the number of geometric isomorphism classes of geometrically irreducibl ...

International Press2013

On the topological full group of a minimal Cantor Z2-system

Nicolas Monod, Gábor Elek

Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor Z-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the negative by prod ...

2013

Non-Supramenable Groups Acting On Locally Compact Spaces

Nicolas Monod, Julian Kellerhals

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...

Univ Bielefeld2013

Uncoupled photonic band gaps

We theoretically investigated the symmetry properties of the modes in two-dimensional square lattice photonic crystals in order to study phenomena that would enable new frontiers in the applications of photonic crystals. Using group theory, symmetry analys ...

Elsevier Science Bv2012

Symmetry Elevation and Symmetry Breaking: Keys to Describe and Explain Excitonic Complexes in Semiconductor Quantum Dots

Elyahou Kapon, Alok Rudra, Marc-André Dupertuis, Daniel Oberli

The results of a group theoretical analysis of the excitonic fine structure are presented and compared with spectroscopic data on single quantum dots. The spectral features reveal the signatures of a symmetry higher than the crystal symmetry (C-3v). A cons ...

Amer Inst Physics, 2 Huntington Quadrangle, Ste 1No1 D, Melville, Ny 11747-4501 Usa2011

A note on topological amenability

Nicolas Monod

A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...

Oxford University Press2010

Order-Optimal Consensus Through Randomized Path Averaging

Martin Vetterli, Patrick Thiran, Florence Bénézit

Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust mes- sage-passing schemes for distributed information processing over networks. However, for many topologies that are realistic for wire- less ...

Institute of Electrical and Electronics Engineers2010

Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

Marc-André Dupertuis, Sascha Dalessi

A general formalism for the maximal symmetrization and reduction of fields (MSRFs) is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and ...

2010

The Dixmier problem, lamplighters and Burnside groups

Nicolas Monod

J.Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Fur ...

2010