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401-3110-20L 4 Credits BSC , MSC D-MATH

Quadratic Forms, Markov Numbers and Diophantine Approximation

Lecturers & Examiners: Dr. Paloma Bengoechea Duro
Number of participants limited to 22.
VVZ CR n/a

Last Updated: 2026-02-05 15:41:20

Abstract

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.

Content

Continued 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

Resources

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
06.01.2020
Signup End
12.02.2020
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Quadratic Forms, Markov Numbers and Diophantine Approximation
  • Thu 15:15-17:00 (HG G 26.1)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and afterwards choose an alternative seminar.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (This semester, many seminars have a waiting list with special selection procedure. If no other criteria apply, a definitive registration will be granted first of all to students who haven't got another seminar registration. Here is the best procedure for dealing with two waiting lists: first choose your preferred seminar and afterwards choose an alternative seminar.)