This project in pure mathematics at University of Helsinki focuses on analysis on metric spaces and its applications in geometry. A central problem is which weak conditions imply the ability to represent a space in some classical form. These representation problems have natural connections to computer science and random processes in physics. The goal of this research is to deepen the understanding of analytic properties related to these problems and to apply them to open problems in geometry. A particular focus will be placed on recently developed qualitative tools, and turning them quantitative, resulting in many natural applications. For example, differentiation and limits are qualitative notions, while exact error bounds make them quantitative. This research relates to and has applications to geometric measure theory, harmonic analysis, theory of partial differential equations and fractal geometry.

2020

2023