7 citations · 31 across the 23 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
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…