Inaugural lecture with Damian Osajda

Inaugural lecture by Damian Osajda

Program:

14.00-14.45 Inaugural lecture

14.50-15.30 Reception

Nonpositive curvature in Geometric Group Theory

Abstract: Despite the fancy terminology, "Nonpositive Curvature" (NPC) in the title refers to local conditions on a metric space that imply asphericity—that is, contractibility of its universal cover. In this talk, I will focus on combinatorial variants of non-positive curvature (CNPC), that is, where the space is a complex (typically polyhedral or simplicial), and the conditions are expressed in terms of the complex's combinatorial properties.

In Geometric Group Theory, we study groups by exploring their actions on spaces—whether on metric spaces (via isometries) or complexes (via automorphisms). Equipping a space with a (C)NPC structure often reveals strong properties of the associated groups. I will discuss applications of (C)NPC both in deepening our understanding of classical families of groups and in constructing new examples of groups with prescribed (and often unexpected) properties.