7 citations · 31 across the 23 of their papers we have counts for
29 papers
Property (T) for random groups in the density model with
Izhar Oppenheim
We prove that random groups in the Gromov density model (under a certain divisibility condition) have property (T) asymptotically almost surely for any density . T…
Non-Abelian expansion of congruence KMS complexes
Izhar Oppenheim, Inga Valentiner-Branth
Coboundary expansion with non-Abelian coefficients is a strong version of high-dimensional expansion for simplicial complexes. One motivation for studying this notion is that it wa…
New cosystolic high-dimensional expanders from KMS groups
Izhar Oppenheim, Inga Valentiner-Branth
Cosystolic expansion is a high-dimensional generalization of the Cheeger constant for simplicial complexes. Originally, this notion was motivated by the fact that it implies the to…
Coboundary expansion of coset complexes
Tali Kaufman, Izhar Oppenheim, Shmuel Weinberger
Coboundary expansion is a high dimensional generalization of the Cheeger constant to simplicial complexes. Originally, this notion was motivated by the fact that it implies topolog…
Property (T) for groups acting on affine buildings
Izhar Oppenheim
We prove that a group acting geometrically on a thick affine building has property (T). A more general criterion for property (T) is given for groups acting on partite complexes.
Banach fixed point property for Steinberg groups over commutative rings
Izhar Oppenheim
The main result of this paper is that all affine isometric actions of higher rank Steinberg groups over commutative rings on uniformly convex Banach spaces have a fixed point. We c…
Banach property (T) for and its applications
Izhar Oppenheim
We prove that a large family of higher rank simple Lie groups (including for ) and their lattices have Banach property (T) with respect to all sup…
Banach Zuk's criterion for partite complexes with application to random groups
Izhar Oppenheim
We prove a Banach version of Żuk's criterion for groups acting on partite simplicial complexes. Using this new criterion we derive a new fixed point theorem for random groups in th…
High dimensional expansion implies amplified local testability
Tali Kaufman, Izhar Oppenheim
In this work we show that high dimensional expansion implies locally testable code. Specifically, we define a notion that we call high-dimensional-expanding-system (HDE-system). Th…
Garland's method with Banach coefficients
Izhar Oppenheim
We prove a Banach version of Garland's method of proving vanishing of cohomology for groups acting on simplicial complexes. The novelty of this new version is that our new conditio…
Curvature criterion for vanishing of group cohomology
Zohar Grinbaum-Reizis, Izhar Oppenheim
We introduce a new geometric criterion for vanishing of cohomology for BN-pair groups. In particular, this new criterion yields a sharp vanishing of cohomology result for all BN-pa…
Coboundary and cosystolic expansion from strong symmetry
Tali Kaufman, Izhar Oppenheim
Coboundary and cosystolic expansion are notions of expansion that generalize the Cheeger constant or edge expansion of a graph to higher dimensions. The classical Cheeger inequalit…
Non p-norm approximated Groups
Alexander Lubotzky, Izhar Oppenheim
It was shown in a previous work of the first named author with De Chiffre, Glebsky and Thom that there exists a finitely presented group which cannot be approximated by almost-homo…
Local Spectral Expansion Approach to High Dimensional Expanders Part II: Mixing and Geometrical overlapping
Izhar Oppenheim
In this paper, we further explore the local-to-global approach for expansion of simplicial complexes that we call local spectral expansion. Specifically, we prove that local expans…
High dimensional expanders and coset geometries
Tali Kaufman, Izhar Oppenheim
High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan comple…
Local spectral expansion approach to high dimensional expanders part I: Descent of spectral gaps
Izhar Oppenheim
This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the conditio…
High Order Random Walks: Beyond Spectral Gap
Tali Kaufman, Izhar Oppenheim
We study high order random walks in high dimensional expanders; namely, in complexes which are local spectral expanders. Recent works have studied the spectrum of high order walks…
Angle criteria for uniform convergence of averaged projections and cyclic or random products of projections
Izhar Oppenheim
We apply a new notion of angle between projections to deduce criteria for uniform convergence results of the alternating projections method under several different settings: averag…
Vanishing of cohomology with coefficients in representations on Banach spaces of groups acting on Buildings
Izhar Oppenheim
We prove vanishing of cohomology with coefficients in representations on a large class of Banach spaces for a group acting "nicely" on a simplicial complexes based on spectral prop…
Averaged projections, angles between groups and strengthening of property (T)
Izhar Oppenheim
Using the method of averaged projections and introducing a new notion of angles between projections, we establish a criterion for a certain type of strengthening of property (T) (w…
Isoperimetric Inequalities and topological overlapping for quotients of Affine buildings
Izhar Oppenheim
We prove isoperimetric inequalities for quotients of -dimensional Affine buildings. We use these inequalities to prove topological overlapping for the 2-dimensional skeletons of…
High dimensional analogue of metric distortion for simplicial complexes
Izhar Oppenheim
We suggest a new possible high dimensional analogue to metric distortion. We then show a possible method for providing lower bounds to this distortion and use this method to prove…
Local spectral expansion approach to high dimensional expanders
Izhar Oppenheim
This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We show the condition of local…
Surface subgroups for lattices in Fuchsian buildings
David Constantine, Jean-Francois Lafont, Izhar Oppenheim
We consider finite 2-dimensional polyhedral complexes, equipped with piecewise non-positively curved, locally CAT(0) metrics. We give conditions on the complex X that ensure that i…