Related papers: Kazhdan's Property (T) for Graphs

Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably…

In this paper we continue our study of property (RD) for Hecke pairs initiated in (V. Shirbisheh, Property (RD) for Hecke pairs. Mathematical Physics, Analysis and Geometry, vol. 15, no. 2, (2012), 173--192). We study the behavior of…

Shalom characterized property (T) in terms of the vanishing of all reduced first cohomology. We characterize group pairs having the property that the restriction map on all first reduced cohomology vanishes. We show that, in a strong sense,…

We first prove the Grinberg-Kazhdan formal arc theorem without any assumptions on the characteristic. This part of the article is equivalent to arXiv:math-AG/0203263. Then we try to clarify the geometric ideas behind the proof by…

This work concerns the study of properties of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain…

This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, which can be thought of as being a kind of discrete Laplacian, and we first discuss…

We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate…

We survey the recent developments concerning fixed point properties for group actions on Banach spaces. In the setting of Hilbert spaces such fixed point properties correspond to Kazhdan's property (T). Here we focus on the general,…

The well-known theorem of Shalom--Vaserstein and Ershov--Jaikin-Zapirain states that the group $\mathrm{EL}_n(\mathcal{R})$, generated by elementary matrices over a finitely generated commutative ring $\mathcal{R}$, has Kazhdan's property…

In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…

The new graph parameter twin-width, introduced by Bonnet, Kim, Thomass e and Watrigant in 2020, allows for an FPT algorithm for testing all FO properties of graphs. This makes classes of efficiently bounded twin-width attractive from the…

Cassidy, Phan and Shelton associate to any regular cell complex X a quadratic K-algebra R(X). They give a combinatorial solution to the question of when this algebra is Koszul. The algebra R(X) is a combinatorial invariant but not a…

Given a countable group $G$, let ${\rm L}(G)$ denote its von Neumann algebra. For a wide class of ICC groups with Kazhdan's property (T), we confirm a conjecture of V.F.R. Jones asserting that $Out(\text{L}(G))\cong Char (G)\rtimes Out(G)$.…

We consider minimal, aperiodic symbolic subshifts and show how to characterize the combinatorial property of bounded powers by means of a metric property. For this purpose we construct a family of graphs which all approximate the subshift…

Property A introduced by Guoliang Yu is an amenability-type property for metric spaces. In this article, we study property A for uniformly locally finite coarse spaces. Main examples of coarse spaces are a metric space, a set equipped with…

Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

The Kazhdan-Lusztig parameters are important parameters in the representation theory of $p$-adic groups and affine Hecke algebras. We show that the Kazhdan-Lusztig parameters have a definite geometric structure, namely that of the extended…

This is mainly an expository text on the Haagerup property for countable groupoids equipped with a quasi-invariant measure, aiming to complete an article of Jolissaint devoted to the study of this property for probability measure preserving…

Given a simple Lie group $G$, we show that the lattices in $G$ are weakly uniformly discrete. This is a strengthening of the Kazhdan-Margulis theorem. Our proof however is straightforward --- considering general IRS rather than lattices…