Split real Kac-Moody symmetric spaces have been introduced and studied by Freyn, Hartnick, Horn and the PI. One key property is boundary rigidity: there is a one-to-one correspondence between the automorphisms of a split real Kac-Moody symmetric space and the automorphisms of the twin building embedded in the future and past causal directions of the boundary.
One goal of this project is to generalize boundary rigidity to complex Kac-Moody symmetric spaces and to use Galois descent in order to introduce and study almost split real Kac-Moody symmetric spaces.
Furthermore, Freyn, Hartnick, Horn and PI have established that the question whether the causal structure of a split real Kac-Moody symmetric admits time travel is equivalent to the question whether Kostant convexity fails for Kac-Moody groups. Conjecturally, Kostant convexity holds and, thus, time travel is impossible in Kac-Moody symmetric spaces. Another goal of this project is to confirm this conjecture.