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 second session of this mini course will take place on Wednesday, January 18 from 3:00 pm – 4:00 pm; the third session of this mini course will take place on Thursday, January 19 from 9:30 am – 10:30 am; the fourth session of this mini course will take place on Friday, January 20 from 1:30 pm – 2:30 pm.