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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > MAX HOPKINS:
All reports by Author Max Hopkins:

TR21-169 | 24th November 2021
Mitali Bafna, Max Hopkins, Tali Kaufman, Shachar Lovett

Hypercontractivity on High Dimensional Expanders: a Local-to-Global Approach for Higher Moments

Hypercontractivity is one of the most powerful tools in Boolean function analysis. Originally studied over the discrete hypercube, recent years have seen increasing interest in extensions to settings like the $p$-biased cube, slice, or Grassmannian, where variants of hypercontractivity have found a number of breakthrough applications including the resolution of ... more >>>


TR20-170 | 9th November 2020
Max Hopkins, Tali Kaufman, Shachar Lovett

High Dimensional Expanders: Random Walks, Pseudorandomness, and Unique Games

Revisions: 1

Higher order random walks (HD-walks) on high dimensional expanders have played a crucial role in a number of recent breakthroughs in theoretical computer science, perhaps most famously in the recent resolution of the Mihail-Vazirani conjecture (Anari et al. STOC 2019), which focuses on HD-walks on one-sided local-spectral expanders. In this ... more >>>




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