Associate 2015-16

Yuliy Baryshnikov


Baryshnikov imageApplied Configuration Spaces

The project deals with Applied Configuration Spaces, an area in Applied Topology, a fast developing part of Algebraic Topology.

Algebraic topology was born as a supporting discipline, aimed at creating a foundation for intuitive notions immensely useful in dynamical systems and complex analysis,dealing with shapes defined up to very broadly understood reparametrizations or continuous deformations.

The development of the area over the course of the twentieth century saw an enormous amount of groundbreaking and beautiful discoveries, ever trending towards more and more abstract apparatus. Nevertheless, algebraic topology remains indispensable for many several communities neighboring mathematics, such as biology, engineering, computer science, data analysis, economics, to name a few.

The past decade has seen a surge of renewed interest in applied topology. Some of the developments (such as Topological Data Analysis) were amply documented; some others, including the areas of applied topology more related to physical, not virtual world, are in need of summarizing monograph. The goal of this project is to fill that broad gap.