23 citations · 98 across the 30 of their papers we have counts for
18 papers · 1 filter
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…
No Where to Go But High: A Perspective on High Dimensional Expanders
Roy Gotlib, Tali Kaufman
"No Where to go but in" is a well known statement of Osho. Osho meant to say that the answers to all our questions should be obtained by looking into ourselves. In a paraphrase to…
Fine Grained Analysis of High Dimensional Random Walks
Roy Gotlib, Tali Kaufman
One of the most important properties of high dimensional expanders is that high dimensional random walks converge rapidly. This property has proven to be extremely useful in variet…
On Good -Query Locally Testable Codes from Sheaves on High Dimensional Expanders
Uriya A. First, Tali Kaufman
We expose a strong connection between good -query locally testable codes (LTCs) and high dimensional expanders. Here, an LTC is called good if it has constant rate and linear di…
The Cheeger Inequality and Coboundary Expansion: Beyond Constant Coefficients
Uriya A. First, Tali Kaufman
The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, nam…
Eigenstripping, Spectral Decay, and Edge-Expansion on Posets
Jason Gaitonde, Max Hopkins, Tali Kaufman +2
We study the relationship between the underlying structure of posets and the spectral and combinatorial properties of their higher-order random walks. While fast mixing of random w…