WORKSHOP 1
Boundaries of Groups (event 1906)
Dates: 1822 June 2018
Place: CIRM (Marseille Luminy, France)
Boundaries of Groups (event 1906)
Dates: 1822 June 2018
Place: CIRM (Marseille Luminy, France)
Description
This workshop aims to address the following topics regarding the boundaries of hyperbolic, relatively hyperbolic and CAT(0) groups. Cannon’s Conjecture and related conjectures: If a torsionfree hyperbolic group group has boundary at infinity a 2sphere, must the group be a lattice in SO(3, 1)? This is one of the remaining outstanding problems in 3dimensional topology. Some related work was done by KapovichKleiner (boundary a Sierpinski carpet). Higher dimensional topological analogues are known (BartelsLückReich, LafontTshishiku). Relation to QIs: In some cases, properties of the boundary can be used to “fill in” and obtain rigidity results about spaces. For example BonkSchramm related the existence of biLipschitz homeomorphism of boundaries to the existence of almostisometries between spaces. CAT(0) boundaries: A famous example of CrokeKleiner shows that the boundary at infinity of a CAT(0) space is not a QIinvariant. However, recent work of Charney Sultan shows that certain subsets of the boundary are QIinvariant. Are there other naturally definite subsets of the boundary that are QIinvariant? Boundaries of Hyperbolic Buildings: These provide an important testing ground for studying metric properties of the boundary. Relatively hyperbolic groups: What is the “best” boundary for a relatively hyperbolic group? The boundary of the hyperbolic space on which the group acts geometrically finitely (known as the Bowditch boundary)? A CAT(0) type boundary? Is there a way to put a quasiconformal structure that is meaningful on either of these boundaries? Rigidity: What group theoretical information can be obtained from the topology of the boundary? 
Scientific Committee
Organizing Committee
List of Speakers & participants

NB: In accordance with the Statement of Inclusiveness (http://www.math.toronto.edu/~rafi/statement/) this event will be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity.