Abstract: Higher Segal spaces, as introduced by Dyckerhoff and Kapranov, are simplicial spaces which obey combinatorial locality conditions governed by polyhedral decompositions of cyclic polytopes. Amongst other places, higher Segal spaces have found applications in homological mirror symmetry and the theory of higher categories. In this talk I will introduce a relative notion of higher Segal spaces and focus on one particular aspect of the theory- the construction of categorified Hall algebra representations.