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SUMMARY:Quantized rational numbers\, from every angles
DTSTART:20250430T120000Z
DTEND:20250430T130000Z
DTSTAMP:20260504T201300Z
UID:indico-event-14309@indico.math.cnrs.fr
CONTACT:kellendonk@math.univ-lyon1.fr
DESCRIPTION:Speakers: Perrine Jouteur (Reims)\n\nQuantum analogues of real
  numbers are a generalization of q-deformed integers (also called Gaussian
  q-integers)\, which consist of replacing integers by polynomials in a for
 mal variable "q"\, in such a way that the specialization q=1 is the initia
 l number. This idea gives rise for example to generating series\, and was 
 already used by Euler to solve combinatorial problems. A good deformation 
 must be compatible with the structural properties of the object that is be
 ing quantized. For instance\, q-deformed binomial coefficients have a quan
 tized Pascal rule.In 2020\, Sophie Morier-Genoud and Valentin Ovsienko pro
 posed a quantization of rational numbers\, generalizing the q-deformed int
 egers\, with good combinatorial properties. In this talk\, we will define 
 these q-rational numbers by three different (but equivalent) ways\, first 
 via continued fractions\, then via the Farey graph\, and finally via an ac
 tion of the modular group. Then we will explain how this last definition d
 iscloses a new version of quantized rational numbers\, known as the left o
 ne (in opposition to the previous q-deformed rational numbers\, called the
  right ones)\, and we will extend the quantized action of the modular grou
 p to unify the left and the right versions.If there is time left\, we will
  have a glimpse on the relationship between quantized rational numbers and
  the braid theory\, and how this relationship can suggest some multidimens
 ional quantized rational numbers. \n\nhttps://indico.math.cnrs.fr/event/1
 4309/
LOCATION:112 (Bat. Braconnier)
URL:https://indico.math.cnrs.fr/event/14309/
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