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Martin Aigner: From Irrational Numbers to Perfect Matchings: 100 Years of Markov’s Uniqueness Problem

Martin Aigner, Freie Universität, Berlin

Time: Wed 2012-10-10 14.15 - 16.15


Location: Oskar Klein auditorium, Alba Nova

Schedule

14:15-15:00: Precolloquium for PhD and master students by Erik Aas.

15:15-16:15: Colloquium lecture by Martin Aigner.

16:15-17:00: Coffee and SMC social get-together.

Abstract (Colloquium)

A celebrated result in number theory is the Theorem of Markov which relates two seemingly totally different subjects: approximations of irrational numbers and the solutions of a certain equation. A proof, which Markov only sketched, was provided in detail by Frobenius precisely 100 years ago. In his paper Frobenius almost casually mentioned a problem, now known as the Uniqueness Conjecture, which has remained unsolved to this day. I will tell you about the Theorem and the Conjecture, and the amazing connections to other fields such as trees, groups, combinatorics of words, lattice paths, and matchings of plane graphs.

No knowledge in number theory or discrete mathematics beyond the basic courses is required to understand everything in the talk.

Title Date
Hendrik Lenstra: Escher and the Droste effect Dec 12, 2012
Bo Berndtsson: Complex Brunn-Minkowski theory Nov 21, 2012
Martin Aigner: From Irrational Numbers to Perfect Matchings: 100 Years of Markov’s Uniqueness Problem Oct 10, 2012
Vladimir Rokhlin: Accurate Randomized Algorithms of Numerical Analysis May 19, 2012
Martin R. Bridson: Discrete groups: A story of geometry, complexity, and imposters Apr 11, 2012
Mats Gyllenberg: Rock, scissors, paper — what a children's game can tell us about evolution Mar 14, 2012
Persi Diaconis: Who Needs Positivity? Feb 10, 2012