This tutorial focuses on the use of discrete Fourier analysis and its higher-order generalisations as a tool for decomposing any bounded function into a structured and a pseudorandom part. Several number-theoretic applications of such decompositions will be presented, together with an account of recent developments which do not fit neatly into the traditional structure-pseudorandomness dichotomy.

The first session of this mini course will take place on Tuesday, January 17 from 4:30 pm – 5:30 pm; the third session of this mini course will take place on Thursday, January 19 from 3:00 pm – 4:00 pm; the fourth session of this mini course will take place on Friday, January 20 from 4:30 pm– 5:30 pm.