Lecturer

Paloma Bengoechea Duro

Coordinator

Subhajit Jana

Time and place

Thursdays 15:00-17:00 at HG G 26.1

Content

In 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.

Tentative topics include: Continued fractions; representation of real numbers by rationals; Hurwitz's theorem; Lagrange spectrum; badly approximable numbers; Schmidt's game; binary quadratic forms; Markov numbers; Markov tree; hyperbolic plane; geometric interpretation of Markov numbers; Ford circles and Farey tessellation; the still open Unicity Conjecture.

Here is a list of contents and references.

Talks