Colloquium abstracts

Ralf Koehl
Justus Liebig University Giessen, Germany
April 18, 2019

The geometry of Kac-Moody groups:  Kac and Peterson introduced a topology on real Kac-Moody groups that is very suitable for their study. Hartnick, K. and Mars proved that this topology turns their twin building into a topological twin building in the sense of Kramer. More recently, Freyn, Hartnick, Horn, K. constructed Kac-Moody symmetric spaces that share many properties with Riemannian symmetric spaces but also allow for new features such as their twin building at infinity, one into a future direction, the other into a past direction. It is my firm belief that this Kac-Moody symmetric space is the natural geometry for the further study of arithmetic Kac-Moody groups -- the geometry of the twin building seems a little sparse, although it still was sufficient for Farahmand Parsa, Horn, K. to establish strong rigidity and superrigidity properties of arithmetic Kac-Moody groups.