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SUMMARY:Some new results in higher order Fourier analysis
DTSTART:20260717T121500Z
DTEND:20260717T134500Z
DTSTAMP:20260913T025000Z
UID:indico-event-1484@math-events.uni-bonn.de
DESCRIPTION:Speakers: Luka Milićević (Mathematical Institute of the Serb
 ian Academy of Sciences and Arts)\n\nAbstract: \nHigher order Fourier ana
 lysis is a generalization of the classical Fourier analysis in which the r
 ole of linear phases is played by polynomial phases and related objects. I
 t originates from the work of Gowers in which he proved quantitative bound
 s in Szemerédi's theorem on arithmetic progressions and introduced a fami
 ly of norms on functions on an abelian group\, now known as the uniformity
  norms. These norms\, denoted by $U^k$ for $k \\ge 2$\, are the central ob
 jects of study in this subject and a key question is the inverse problem\,
  which is to understand the structure of functions with a large value of u
 niformity norm. \nIn this talk\, I will present some novel results in thi
 s field: a general inverse theory for the $U^4$ norm\, as well as a joint 
 work with Žarko Ranđelović\, in which we prove that the Möbius functio
 n does not correlate with polynomial phases in function fields over prime 
 fields. \n \n\nhttps://math-events.uni-bonn.de/event/1484/
LOCATION: Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1484/
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