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SUMMARY:Polynomial maps between abelian groups
DTSTART:20260522T121500Z
DTEND:20260522T134500Z
DTSTAMP:20260526T042400Z
UID:indico-event-1337@math-events.uni-bonn.de
DESCRIPTION:Speakers: Elias Schuster (University of Bonn)\n\nAbstract: \n
 Using discrete derivatives\, one can define a notion of polynomials betwee
 n arbitrary groups. Such polynomials arise naturally in inverse Gowers the
 ory through a fundamental (and still only partially established) dichotomy
 : a bounded function $f \\colon G \\to \\mathbb{C}$ either behaves pseudor
 andomly\, or it correlates with a polynomial phase. This principle is cruc
 ial in establishing the existence of arithmetic patterns in subsets $A \\s
 ubset G$.\nDespite their importance\, polynomial maps are only partially u
 nderstood yet. To remedy this\, it is valuable to develop algebraic charac
 terizations of such functions. In this talk\, we describe the construction
  of a universal group $\\textup{Pol}_k^{ab}(G)$ which classifies all unita
 l polynomials of degree at most $k$ from $G$ into an abelian group\, build
 ing on work of Jamneshan and Thom. We then present classification results 
 of $\\textup{Pol}_k^{ab}(G)$ for a large class of abelian groups $G$. \n
  \n\nhttps://math-events.uni-bonn.de/event/1337/
LOCATION:Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1337/
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