'Singularity' often refers to a phenomenon where the usual (or classical) description of the object under study breaks down. In geometric analysis, this means geometric objects - 'shapes' - that cannot be described as smooth objects, and where our usual geometric intuition possibly fails. For such singular objects new, non-smooth, analytic and geometric tools must be invented and used. The structure of singular, or non-smooth, geometries has gained importance in recent decades, not only as a limiting case of classical theory, but also in its own right, as a natural part of the world around us or, in the case of this project, of the mathematical landscape of geometric analysis. This project, titled 'Structure of Singular Spaces' and carried out in the University of Jyväskylä, develops several aspects of structural results using new insights from modern geometric measure theory and non-smooth analysis, and explores further exotic examples of singular spaces.

2023

2027