Asymptotic-safety inspired results and ideas in causal set quantum gravity
I will argue that a fruitful strategy to make progress in quantum gravity is to connect distinct approaches and transfer methods and ideas from one approach to another. As a concrete example, I will explain recent results in causal-set quantum gravity. The first, namely the construction of a higher-order curvature operator in causal sets, is motivated by the idea to use causal sets as a Lorentzian regularization of the gravitational path integral, in which one can search for asymptotic safety. The second, namely an upper bound on the mass of scalars is inspired by the "matter matters" program in asymptotically safe quantum gravity, in which observational tests of quantum gravity are based on gravity's interplay with matter. I will argue that a similar program for causal sets can provide new, observationally motivated constraints on causal set quantum gravity.To provide background and motivation for these results, I'll provide brief and pedagogical introductions into the key features and key open challenges of both asymptotically safe quantum gravity as well as causal set quantum gravity.