The purpose of this project is to apply modern methods of mathematical analysis to study the shapes of non-smooth and fractal spaces. While the setting is abstract, our research is closely connected to current and concrete problems such as facial recognition. We search for conformal and quasiconformal coordinates, that is, mappings that distort small shapes as little as possible. Our research concerns classical mapping problems that remain unsolved after more than a hundred years, as well as modern applications of mapping theory such as the classifications of abstract algebraic structures and dynamical systems. The site of research is the University of Jyväskylä.

2024

2028