# Improving the bounds for Roth's theorem

From Polymath1Wiki

This is a holding page for a wiki for Polymath6, a project that aims to look at recent results of Bateman and Katz and of Sanders, and attempt to combine the ideas that go into them in order to break the log N-barrier in Roth's theorem. I hope that soon there will be expositions of their proofs, as well as of much of the background material needed to understand them.

## Annotated bibliography

- Michael Bateman and Nets Katz, New bounds on cap sets. The paper that obtains an improvement to the Roth/Meshulam bound for cap sets.

- Tom Sanders, On Roth's theorem on progressions. The paper that gets within loglog factors of the 1/logN density barrier in Roth's theorem.