Thomaths 30 : Nombres Quantiques

In this undergraduate video, Alex discusses the recent work of S. Morier-Genoud and V. Ovsienko on the deformation of numbers and their properties. 0:00 Introduction 0:51 I- Quantum Integers 5:41 II- Symmetry of Rationals 11:14 III- Quantum Rationals and Irrationals 18:17 IV- Another Deformation References/For further reading: Articles by S. Morier-Genoud and V. Ovsienko "q-deformed rationals and q-continued fractions", Forum Math. Sigma 8 (2020), 55 pp., https://arxiv.org/pdf/1812.00170 "On q-deformed real numbers", Experimental. Math. 31 (2022), no. 2, pp. 652-660, https://arxiv.org/pdf/1908.04365 INSMI blog "Quantum numbers? Surely you're joking, Mr. Feynman!": https://www.insmi.cnrs.fr/fr/cnrsinfo... My article "Infinitesimal modular group: q-deformed sl2 and Witt algebra", SIGMA 20 (2024), 053, https://arxiv.org/pdf/2308.06158.pdf If you appreciate our work, you can support us at https://fr.tipeee.com/thomaths or at https://fr.liberapay.com/Thomaths/ ! THANK YOU All images were created specifically for this episode.