Review: Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture (H.Huang, 2019)

1. (speaker - A.A. Valyuzhenich) Review of the paper "Hao Huang, Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture, Annals of Mathematics, 190 (2019) 949-955@, https://doi.org/10.4007/annals.2019.190.3.6 2. (speaker - I.Yu. Mogilnykh) In the work of Valyuzhenich and Mogilnykh (2020) it was established that every perfect 2-coloring of $H(n,q)$ with the second eigenvalue is reduced (by removing fictitious positions) to a perfect 2-coloring of $H(3,q)$, except for two constructions. Earlier Vorobeev obtained a construction of perfect 2-colorings of $H(3,q)$ with external degree (parameter from the coloring matrix) $>q/2$. The report will consider a construction that combines the idea of ​​Vorob'ev's construction and an approach through substitutional switchings (Valyuzhenich and Mogilnykh, 2020). This method allows one to construct colorings with an arbitrarily small odd external degree with a sufficiently large cardinality of the alphabet q.