Languages of higher dimensional automata and Kleene theorem

Higher dimensional automata (HDA) are a formalism for modeling concurrent systems introduced by Pratt and van Glabbeek. I will present several ways to define languages of HDA, which are collections of interval pomsets closed under subsumption. Then I will define regular interval pomset languages and formulate Kleene theorem for HDA. Finally, I will sketch its proof, which employs some ideas derived from topology and geometry.