| Résume | Markov triples forming an infinite set of triples of natural numbers were introduced by Markov as a part of his study of relation between real binary quadratic forms and the square lattice. Frobenius conjecture, remaining open for more than one hundred years, has acquired numerous reformulations in various contexts; in its original formulation, it states that the maximal element of a Markov triple determines the remaining two numbers in this triple. In my talk, i will tell about two other equivalent statements in the tropical context recently obtained by Kevin Calderon: the first one is given via tropical cotangents of angles formed by two tangents to Markov hyperbolas, and the other one is a conjectural statement about tropical wave fronts of Markov triangles. |
