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04/20/2023
No Where to Go But High: A Perspective on High Dimensional Expanders
"No Where to go but in" is a well known statement of Osho. Osho meant to...
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11/17/2022
Double Balanced Sets in High Dimensional Expanders
Recent works have shown that expansion of pseudorandom sets is of great ...
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11/17/2022
Unique-Neighbor-Like Expansion and Group-Independent Cosystolic Expansion
In recent years, high dimensional expanders have been found to have a va...
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10/27/2022
List Agreement Expansion from Coboundary Expansion
One of the key components in PCP constructions are agreement tests. In a...
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08/05/2022
Beyond the Worst Case: Structured Convergence of High Dimensional Random Walks
One of the most important properties of high dimensional expanders is th...
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08/02/2022
On Good 2-Query Locally Testable Codes from Sheaves on High Dimensional Expanders
We expose a strong connection between good 2-query locally testable code...
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08/02/2022
Couboundary Expansion of Sheaves on Graphs and Weighted Mixing Lemmas
We study the coboundary expansion of graphs, but instead of using 𝔽_2 as...
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05/02/2022
Eigenstripping, Spectral Decay, and Edge-Expansion on Posets
Fast mixing of random walks on hypergraphs has led to myriad breakthroug...
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02/17/2022
Improved Optimal Testing Results from Global Hypercontractivity
The problem of testing low-degree polynomials has received significant a...
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11/17/2021
Hypercontractivity on High Dimensional Expanders: a Local-to-Global Approach for Higher Moments
Hypercontractivity is one of the most powerful tools in Boolean function...
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11/03/2021
Scalar and Matrix Chernoff Bounds from ℓ_∞-Independence
We present new scalar and matrix Chernoff-style concentration bounds for...
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07/22/2021
High dimensional expansion implies amplified local testability
In this work we show that high dimensional expansion implies locally tes...
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01/29/2021
Local to global high dimensional expansion and Garland's method for general posets
In simplicial complexes it is well known that many of the global propert...
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11/09/2020
High Dimensional Expanders: Random Walks, Pseudorandomness, and Unique Games
Higher order random walks (HD-walks) on high dimensional expanders have ...
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08/21/2020
Quantum LDPC codes with Ω(√(n)log^kn) distance, for any k
In this work we construct quantum LDPC codes of distance √(n)log^k n for...
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04/16/2020
Decodable quantum LDPC codes beyond the √(n) distance barrier using high dimensional expanders
Constructing quantum LDPC codes with a minimum distance that grows faste...
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08/01/2018
List Decoding with Double Samplers
We develop the notion of "double samplers", first introduced by Dinur an...
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03/07/2018