2 citations · 2 across the 2 of their papers we have counts for
6 papers
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…
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…
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…
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…