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SUMMARY:Sophie Morier-Genoud (Université Reims Champagne Ardenne)
DTSTART:20220607T123000Z
DTEND:20220607T133000Z
DTSTAMP:20260423T021439Z
UID:OWNS/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/88/">q-
 analogues of real numbers</a>\nby Sophie Morier-Genoud (Université Reims 
 Champagne Ardenne) as part of One World Numeration seminar\n\n\nAbstract\n
 Classical sequences of numbers often lead to interesting q-analogues. The 
 most popular among them are certainly the q-integers and the q-binomial co
 efficients which both appear in various areas of mathematics and physics. 
 With Valentin Ovsienko we recently suggested a notion of q-rationals based
  on combinatorial properties and continued fraction expansions. The defini
 tion of q-rationals naturally extends the one of q-integers and leads to a
  ratio of polynomials with positive integer coefficients. I will explain t
 he construction and give the main properties. In particular I will briefly
  mention connections with the combinatorics of posets\, cluster algebras\,
  Jones polynomials\, homological algebra. Finally I will also present furt
 her developments of the theory\, leading to the notion of q-irrationals an
 d q-unimodular matrices.\n
LOCATION:https://researchseminars.org/talk/OWNS/88/
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