34 citations · 161 across the 29 of their papers we have counts for
31 papers
The Kadets--Werner modification of Bourgain--Rosenthal space is asymptotically midpoint uniformly convex
Florent P. Baudier
Let be the Kadets--Werner modification of a closed subspace of constructed by Bourgain and Rosenthal in 1980. In this short note, it is shown that $X_{\math…
Asymptotic and nonlinear geometries of Banach spaces and their interactions
Florent P. Baudier, Gilles Lancien
This book discusses the interactions between the (nonlinear) metric structure of Banach spaces and their linear asymptotic behavior. The overarching problem is to understand how th…
On asymptotic B-convexity and infratype
Florent Baudier, Audrey Fovelle
In this note, we introduce and study the notions of asymptotic B-convexity and asymptotic infratype , and we prove asymptotic analogs of a series of results due to Giesy \cite{G…
An asymptotic analog of a local-to-global phenomenon for uniformly convex renormings
Florent P. Baudier, Gilles Lancien
In this note, we investigate the renorming theory of Banach spaces with property of Rolewicz. In particular, we give a "coordinate-free" proof of the fact that every Banach s…
On stability of metric spaces and Kalton's property
F. Baudier, Th. Schlumprecht, A. Zsák
The first named author introduced the notion of upper stability for metric spaces as a relaxation of stability. The motivation was a search for a new invariant to distinguish the c…
Coarse equivalence versus bijective coarse equivalence of expander graphs
Florent Baudier, Bruno de Mendonça Braga, Ilijas Farah +2
We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if…
Abstract embeddability ranks
Florent P. Baudier, Christian Rosendal
We describe several ordinal indices that are capable of detecting, according to various metric notions of faithfulness, the embeddability between pairs of Polish spaces. These embe…
Embeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebras
Florent P. Baudier, Bruno de Mendonça Braga, Ilijas Farah +2
We study which von Neumann algebras can be embedded into uniform Roe algebras and quasi-local algebras associated to a uniformly locally finite metric space . Under weak assumpt…
-distortion of Wasserstein metrics: a tale of two dimensions
Florent P. Baudier, Chris Gartland, Thomas Schlumprecht
By discretizing an argument of Kislyakov, Naor and Schechtman proved that the 1-Wasserstein metric over the planar grid has -distortion bounded below by a…
Uniform Roe algebras of uniformly locally finite metric spaces are rigid
Florent P. Baudier, Bruno de Mendonça Braga, Ilijas Farah +3
We show that if and are uniformly locally finite metric spaces whose uniform Roe algebras, $\cstu(X)$ and $\cstu(Y)$, are isomorphic as \cstar-algebras, then and ar…
No dimension reduction for doubling subsets of when revisited
Florent P. Baudier, Krzysztof Swieçicki, Andrew Swift
We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and \cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for doubling subsets of for $q>…
Umbel convexity and the geometry of trees
Florent P. Baudier, Chris Gartland
For every , a new metric invariant called umbel -convexity is introduced. The asymptotic notion of umbel convexity captures the geometry of countably branching t…
Coarse and Lipschitz universality
Florent P. Baudier, Gilles Lancien, Pavlos Motakis +1
In this paper we provide several \emph{metric universality} results. We exhibit for certain classes $\cC$ of metric spaces, families of metric spaces which ha…
The geometry of Hamming-type metrics and their embeddings into Banach spaces
Florent P. Baudier, Gilles Lancien, Pavlos Motakis +1
Within the class of reflexive Banach spaces, we prove a metric characterization of the class of asymptotic- spaces in terms of a bi-Lipschitz invariant which involves metrics…
Stochastic approximation of lamplighter metrics
Florent P. Baudier, Pavlos Motakis, Thomas Schlumprecht +1
We observe that embeddings into random metrics can be fruitfully used to study the -embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces…
On the bi-Lipschitz geometry of lamplighter graphs
Florent P. Baudier, Pavlos Motakis, Thomas Schlumprecht +1
In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes…
A new coarsely rigid class of Banach spaces
Florent Baudier, Gilles Lancien, Pavlos Motakis +1
We prove that the class of reflexive asymptotic- Banach spaces is coarsely rigid, meaning that if a Banach space coarsely embeds into a reflexive asymptotic- space $Y…
The coarse geometry of Tsirelson's space and applications
Florent Baudier, Gilles Lancien, Thomas Schlumprecht
The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space . Every…
Lipschitz Embeddings of Metric Spaces into
Florent P. Baudier, Robert Deville
Let be a separable metric space. We say that is a good--embedding if, whenever , implies and, for each…
On the geometry of the countably branching diamond graphs
Florent P. Baudier, Ryan Causey, Stephen DIlworth +4
In this article, the bi-Lipschitz embeddability of the sequence of countably branching diamond graphs is investigated. In particular it is shown that for…
-distortion of some infinite graphs
Florent P. Baudier, Sheng Zhang
A distortion lower bound of is proven for embedding the complete countably branching hyperbolic tree of height into a Banach space admitting an equivalent no…
Tight embeddability of proper and stable metric spaces
Florent Baudier, Gilles Lancien
We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for , every proper subset of is almost Lipschitz…
On the -distortion of some infinite graphs
Florent Pierre Baudier
We show a distortion lower bound of when embedding the countably branching hyperbolic tree of height into a Banach space with an equivalent norm satisfying R…
Barycentric gluing and geometry of stable metrics
Florent Pierre Baudier
We discuss various aspects of a local-to-global embedding technique and the metric geometry of stable metric spaces and of two of its important subclasses: locally finite spaces an…