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19.05.2020
“Combinatorial nonpositive curvature and group theory”

“Combinatorial nonpositive curvature and group theory”

Damian Osajda (University of Wroclaw)

Colloquium of the Department of Mathematics and Computer Science

Thursday May 21 at 17:15 zoom ID 675-315-555

Abstract

 

Various notions of nonpositive curvature have been explored in recent decades in the frame of Geometric Group Theory. Most influential were the notions of CAT(0) and Gromov hyperbolic spaces. On one hand such spaces and their automorphism groups exhibit a plethora of important geometric, algebraic, and algorithmic features, so that equipping a given object with the structure allows one to conclude many interesting properties. On the other hand, various techniques emerging when studying nonpositive curvature give rise to methods of constructing new – sometimes seemed as exotic – examples. In the talk I will focus on the combinatorial version of nonpositive curvature. This concerns various local combinatorial conditions on simplicial or polyhedral complexes making them behave a bit like CAT(0) spaces. Examples of such complexes and of groups acting on them in a controlled way include: Gromov hyperbolic, small cancellation, CAT(0) cubical, and systolic ones, as well as recent generalization of these notions, which will be the main subject of the talk.

 

Everyone is welcome!