q-analogues of real numbers

Sophie Morier-Genoud (Université Reims Champagne Ardenne)

07-Jun-2022, 12:30-13:30 (22 months ago)

Abstract: Classical sequences of numbers often lead to interesting q-analogues. The most popular among them are certainly the q-integers and the q-binomial coefficients 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 definition of q-rationals naturally extends the one of q-integers and leads to a ratio of polynomials with positive integer coefficients. I will explain the 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 further developments of the theory, leading to the notion of q-irrationals and q-unimodular matrices.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper )


One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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Organizers: Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Niels Langeveld, Lingmin Liao, Wolfgang Steiner*
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