# Dalius Stulga: Provable properties of asymptotic safety in the f(R) approximation

In this talk I will describe how we can derive general properties of the fixed-point solutions to the flow equations in the f(R) approximation using a family of non-adaptive cutoffs. The full f(R) approximation results in complicated differential equations and makes analysis very difficult. However, progress can be made using analytic approaches. Firstly, solving the flow equations asymptotically at large curvature allows us to conclude that there are discrete set of fixed-point solutions. We can then use Sturm-Liouville techniques to draw conclusions about the properties of these fixed points and their eigenoperator spectrum.