Recent applications of topology to computer science model computation-like
things by paths (schedules of concurrent jobs in Directed Algebraic
Topology; proofs of equalities in Homotopy Type Theory). An intuition due to
Robin Gandy is that computations are continuous flows of information, which
suggests another such application: we might dream of a space of assignments
of information over a base space, in which paths correspond to computations.
This talk will present a partial realization of this dream which works only over
weird spaces -- and produces even weirder ones! I hope it has some meaning
in terms of "hyperspaces", which might help improve this situation.