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SUMMARY:Modular deformation of rational numbers and plane geometry
DTSTART:20260903T150000Z
DTEND:20260903T160000Z
DTSTAMP:20260910T060900Z
UID:indico-event-17089@indico.math.cnrs.fr
CONTACT:kellendonk@math.univ-lyon1.fr\;athomas@math.univ-lyon1.fr
DESCRIPTION:Speakers: Perrine Jouteur (MPIS Leipzig)\n\nThe q-analogue of 
 an object is a family of objects indexed by a variable q\, such that the s
 pecialization q->1 gives back the initial object. One of the oldest deform
 ed objects in mathematics are q-integers\, already used by Euler and Gauss
  to solve combinatorial problems. In this talk\, I will present a general
 ization of these q-integers to real numbers\, defined in 2020 by Morier-Ge
 noud and Ovsienko. The theory of q-real numbers is based on a deformed act
 ion of the modular group PSL2(Z) on the real line. I will give a geometric
  interpretation of this q-action\, understanding q-real numbers as geodesi
 cs of the hyperbolic plane. This point of view naturally leads to consider
  new geometric operations on q-rational numbers\, looking at common tangen
 t lines of the geodesics. We will see that these operations have an algebr
 aic counterpart that we call Springborn operations\, and that are quadrati
 c versions of the Farey sum. I will describe a bridge between the geometri
 c and the algebraic settings and highlight how one can use this bridge to 
 deduce structural results on q-rational numbers. This talk is based on a j
 oint work with Olga Paris-Romaskevich and Alexander Thomas.\n\nhttps://ind
 ico.math.cnrs.fr/event/17089/
LOCATION:Salle Fokko du Cloux (Bat. Braconnier)
URL:https://indico.math.cnrs.fr/event/17089/
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