Groups and nonpositive curvature
Navn på bevillingshaver
Damian Osajda
Titel
Assistant Professor
Institution
University of Copenhagen
Beløb
DKK 4,902,329
År
2023
Bevillingstype
Semper Ardens: Accelerate
Hvad?
This research project is in pure mathematics. We will study “groups”. “Group” is a mathematical concept describing symmetries of the object, e.g. of a space, a graph, a polyhedron. It can be thought of as a pattern describing symmetries. Many such patterns – groups are known and studied already for a long time. We intend to give new insight into such classical groups and find new ones.
Hvorfor?
Symmetries are of fundamental importance in our understanding of the Universe, both in macro- and micro-scale. In the first case, the symmetries of time and space are responsible for basic conservation laws, the foundation of modern physics. At the micro level, symmetries of particles determine their chemical features, which e.g. lie at the root of intriguing properties of proteins, or viruses.
Hvordan?
Our approach to studying groups is via the Geometric Group Theory. It is a relatively new area of mathematics employing geometric methods to study groups. A fundamental tool for our approach to groups is “nonpositive curvature”. The notion has its origins in a very classical mathematical field of “Riemannian geometry” seemingly far from the very algebraic context of groups.