Quasipolynomial Bounds for the Corners Theorem

We prove quasipolynomial bounds for the corners theorem for general abelian groups. The proof draws on a number of themes in additive combinatorics, including recent work of Kelley-Meka on 3-term arithmetic progressions, work on almost periodicity, and work of Conlon, Fox, and Zhao on densification.

Based on joint work with Michael Jaber, Yang P Liu, Shachar Lovett and Anthony Ostuni.

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