The ACO Seminar (2023–2024)

We discuss recent improved bounds for Szemerédi’s Theorem. The talk will seek to provide a gentle introduction to higher order Fourier analysis and recent quantitative developments. In particular, the talk will provide a high level sketch for how the inverse theorem for the Gowers norm enters the picture and the starting points for the proof of the inverse theorem. Additionally the talk (time permitting) will discuss how recent work of Leng on equidistribution of nilsequences enters the picture and is used. No background regarding nilsequences will be assumed. Based on joint work with James Leng and Ashwin Sah