A. Valette

activity

20042026

most citedIsometric group actions on Hilbert spaces: growth of cocycles

81 citations · 182 across the 25 of their papers we have counts for

collaborators

29 papers

math.OA2026

The Baum-Connes conjecture: a concise course

Alain Valette

These are the slightly edited notes from a 10-hour course I taught at Institut Henri Poincaré in January-February 2025 in the framework of the thematic semester "Representation the…

math.GR2023

Maximal Haagerup subgroups in $Z^{n + 1} ⋊_{ρ_{n}} G L_{2} (Z)$

Alain Valette

For $n \geq 1$ , let $ρ_{n}$ denote the standard action of $G L_{2} (Z)$ on the space $P_{n} (Z) ≃ Z^{n + 1}$ of homogeneous polynomials of degree $n$ in two variables, with integer coeff…

math.OA2022

Equivariant K-homology and K-theory for some discrete planar affine groups

Ramon Flores, Sanaz Pooya, Alain Valette

We consider the semi-direct products $G = Z^{2} ⋊ G L_{2} (Z), Z^{2} ⋊ S L_{2} (Z)$ and $Z^{2} ⋊ Γ (2)$ (where $Γ (2)$ is the congruence subgrou…

math.GR2022

The exceptional simple Lie group $F_{4 (- 20)}$ , after J. Tits

Alain Valette

This is a semi-survey paper, where we start by advertising Tits' synthetic construction from \cite{Tits}, of the hyperbolic plane $H^{2} (C a y)$ over the Cayley numbers $C a y$ , and of i…

math.MG2021

Wasserstein distance and metric trees

Maxime Mathey-Prevot, Alain Valette

We study the Wasserstein (or earthmover) metric on the space $P (X)$ of probability measures on a metric space $X$ . We show that, if a finite metric space $X$ embeds stochastically…

math.GR2021

On arithmetic properties of solvable Baumslag-Solitar groups

Laurent Hayez, Tom Kaiser, Alain Valette

For $0 < α \leq 1$ , we say that a sequence $(X_{k})_{k > 0}$ of $d$ -regular graphs has property $D_{α}$ if there exists a constant $C > 0$ such that $diam (X_{k}) \geq C \cdot ∣ X_{k} ∣^{α}$ . We i…

The Baum-Connes conjecture: a concise course

Maximal Haagerup subgroups in Zn+1⋊ρn​​GL2​(Z)

Equivariant K-homology and K-theory for some discrete planar affine groups

The exceptional simple Lie group F4(−20)​, after J. Tits

Wasserstein distance and metric trees

On arithmetic properties of solvable Baumslag-Solitar groups

Maximal Haagerup subgroups in $Z^{n + 1} ⋊_{ρ_{n}} G L_{2} (Z)$

The exceptional simple Lie group $F_{4 (- 20)}$ , after J. Tits