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SUMMARY:Arithmetic properties of generalised polynomials [MPIM]
DTSTART:20250430T143000Z
DTEND:20250430T153000Z
DTSTAMP:20260317T065900Z
UID:indico-event-370@math-events.uni-bonn.de
DESCRIPTION:Speakers: Jakub Byszewski (Jagiellonian University\, Krakow)\n
 \nNumber theory lunch seminar\nWe study generalised polynomials\, that is\
 , functions that can be expressed using standard algebraic operations and 
 the floor function. Generalised polynomials have long been studied (both e
 xplicitly and implicitly) in number theory and dynamics\, often using dyna
 mical and ergodic-theoretic methods (especially dynamics on nilmanifolds).
  These methods enable one to deduce precise information about the average 
 behaviour of generalised polynomials\, but allow for complicated behaviour
  on special sets of density zero. We will present some of the classical re
 sults and give examples of various interesting arithmetic and combinatoria
 l behaviour occurring along sets of density zero as well as restrictions t
 o what is possible. We will also state an analogue of Hadamard's quotient 
 theorem for generalised polynomials (the classical version concerns linear
  recurrences). We will also formulate several open problems. The talk is b
 ased on joint work with Jakub Konieczny (Oxford).\n\nhttps://math-events.u
 ni-bonn.de/event/370/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/370/
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