analysis / Harmonic analysis
How large can a measurable $A \subseteq [0,R]^2$ be while avoiding the vertices of upward-oriented axis-aligned right triangles of area $1/2$? At most $O_c(R^2/(\log R)^c)$, with a matching-shaped lower bound construction.
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Append-only history
How large can a measurable $A \subseteq [0,R]^2$ be while avoiding the vertices of upward-oriented axis-aligned right triangles of area $1/2$? At most $O_c(R^2/(\log R)^c)$, with a matching-shaped lower bound construction.
Research memory
How large can a measurable $A \subseteq [0,R]^2$ be while avoiding the vertices of upward-oriented axis-aligned right triangles of area $1/2$? At most $O_c(R^2/(\log R)^c)$, with a matching-shaped lower bound construction.
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