Higher Segal spaces

I will describe joint work in progress with Mikhail Kapranov.
Segal spaces were introduced by C. Rezk as models for higher categories whose composition law is weakly associative up to coherent homotopy. In this talk, we will introduce the notion of a 2-Segal space which is a simplicial space satisfying a weaker locality condition than a (1-)Segal space. We will discuss examples of 2-Segal spaces, such as Waldhausen spaces, explain their relevance for Hall algebra constructions, and outline their basic theory within the context of model categories.