Lecture 8. Kostiantyn Drach: «Fractals, complex dynamics and finding roots of polynomials»
Channel: Projekt MmF
Date: 2023-08-18

In the lecture, I will give a gentle introduction to a modern and fascinating branch of dynamical systems called complex dynamics. This branch studies iterations of functions over complex numbers, and this is where some of the most famous and beautiful fractals, such as the Mandelbrot set, appear. We will explore a connection of this field to numerical root finding methods, and also to Kharkiv. Finally, I will describe some of the active research directions in complex dynamics. There will be a lot of pictures, and the lecture will not require knowing complex numbers. However, you will understand things better if you know them. 

Speaker

Kostiantyn Drach is an outstanding young researcher who works in the fields of dynamical systems, geometric inequalities, and topological data analysis. He is currently a postdoc at the Institute of Science and Technology Austria. Starting in September, Kostya will be an assistant professor at the Universitat de Barcelona in Spain. 

Kostya is a native of Kharkiv. After graduating from the Kharkiv Physics and Mathematic Lyceum No. 27, he obtained his bachelor, master, and doctoral degrees from the V. N. Karazin Kharkiv National University, earning many distinctions on the way.

Incidentally, in joint work with Richard Schwartz, Kostya has given a beautiful new proof of the Seven Circles Theorem based on hyperbolic geometry.