Seminar talk by Prof. Michel Waldschmidt from IMJ-PRG, France

Speaker : Prof. Michel Waldschmidt from IMJ-PRG, France

Title: On the Markoff equation x^2+y^2+z^2=3xyz

Date & Time : 12 December 2023, 1115 AM

Venue : PSB 3105

Abstract : It is easy to check that the equation x^2+y^2+z^2=3xyz, where the three unknowns x, y, z are positive integers, has infinitely many solutions. There is a simple algorithm which produces all of them. However, this does not answer to all questions on this equation: in particular Frobenius asked whether the graph of these solutions is a tree (no loop): it is true that for each integer z>0, there is at most one pair (x,y) such that x< y < z and (x,y,z) is a solution. This question is an active research topic nowadays.