  We give a new proof of logarithmic bounds for Roth's theorem on arithmetic
progressions, namely that if $A \subset \{1,2,\ldots,N\}$ is free of three-term
progressions, then $\lvert A\rvert \leq N/(\log N)^{1-o(1)}$. Unlike previous
proofs, this is almost entirely done in physical space using
almost-periodicity.
