401-3110-20L  Quadratic Forms, Markov Numbers and Diophantine Approximation

SemesterSpring Semester 2020
LecturersP. Bengoechea Duro
Periodicitynon-recurring course
Language of instructionEnglish
CommentNumber of participants limited to 22.


AbstractIn 1880 Andrei A. Markov discovered beautiful connections between minima of binary real quadratic forms, badly approximable numbers by rationals, and a certain Diophantine equation which describes an affine cubic surface, now and days called Markov surface. We will use Markov's theory as a unifying thread to talk about quadratic forms, Diophantine approximation and hyperbolic geometry.
Objective
ContentContinued fractions; representation of real numbers by rationals; Hurwitz's theorem; Lagrange spectrum; badly approximable numbers; binary quadratic forms; Markov numbers; Markov tree; geometric interpretation of Markov numbers; the still open Unicity Conjecture