Geodesic
On Sumsets of Subsets of Squares
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 311-317.

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Let $A\subseteq \{1,\dots ,N\}$ be a set of size $\delta N$. We prove a Bogolyubov–Ruzsa type result that $A^2+A^2+A^2-A^2-A^2-A^2$ contains a large low-dimensional generalized arithmetic progression.
Keywords: additive theorems, squares. 
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     author = {Tomasz Schoen},
     title = {On {Sumsets} of {Subsets} of {Squares}},
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Tomasz Schoen. On Sumsets of Subsets of Squares. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 311-317. http://geodesic.mathdoc.fr/item/TM_2021_314_a14/

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