10th Distinguished Lecture丨Tropical trigonometry, caustics and continued fractions

2024-04-12 11:10:10



主持人:Ivan Fesenko, ITS

主讲人: Grigory Mikhalkin, University of Geneva

主讲人简介:Grigory Mikhalkin is a professor at the University of Geneva in Switzerland. Professor Mikhalkin is one of the founders of and contributors to Tropical Geometry, a domain of algebraic geometry, which has many links with several other areas including mathematical physics.

He was awarded the Prize of the St. Petersburg Mathematical, the Silver Medal of the Mexican Mathematical Society, and the Chair of Fondation Sciences Mathématiques de Paris. He was also an invited speaker at the International Congress of Mathematicians.

报告题目:Tropical trigonometry, caustics and continued fractions

摘要:We'll take a look at geometry and trigonometry of the tropical plane by means of the so-called tropical wave front evolution. As any evolution process in the plane, described by the PDE of the first order, it defines the caustic curve. In this case, the caustic produces a subdivision of the tropical angle to the elementary angles. Surprisingly, it can be seen as a geometric manifestation of the continued fractions, both in the classical form (with plus signs), and in the Hirzebruch-Jung form (with minus signs). Joint work with Mikhail Shkolnikov.