Quadratic Forms, Markov Numbers and Diophantine Approximation Spring 2020

Paloma Bengoechea Duro
Subhajit Jana
Time and place
Thursdays 15:00-17:00 at HG G 26.1


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.


Speakers Date Notes
Igor Krstic February 27 Lecture 1
Roberto Cagnotti March 5 Lecture 2
Elias Dubno March 12 Lecture 3
Donior Akhmedov March 19 Lecture 4
Michael Obergfell March 26 Lecture 5
Charlotte Dombrowsky April 2 Lecture 6
Nadine Merk April 9 Lecture 7
Tiziana Bolsinger April 9 Lecture 7
Ningjie Tan April 23 Lecture 8
Xiao Yang April 30 Lecture 9
Martin Wohlfender May 14 Lecture 10
Sebastian Voegele May 14 Lecture 10