Speaker
Rafael Andrist
(University of Ljubljana)
Description
The Diophantine solutions of the so-called Markov equation $x^2 + y^2 + z^2 = 3xyz$ were originally considered by Markov in 1879. The solutions $(x, y, z)$ in the natural numbers are called Markov triples. Later, this equation was studied over the complex numbers in algebraic geometry: The group of algebraic symmetries is discrete and acts transitively on the Markov triples. Research about the Markov equation has remained a very active area in both number theory and geometry until now. We describe the group of holomorphic symmetries. In contrast to the algebraic case, this group is infinite-dimensional and interpolates any permutation of (ordered) Markov triples.
Author
Rafael Andrist
(University of Ljubljana)
