Asymptotic Safety in the Standard Model and Beyond

We study the evolution of the Standard Model couplings within the framework of Asymptotic Safety in two different settings. First, we explore the dynamics of Gauge-Yukawa systems, which has been proven to be successful in the generation of UV FPs. With an extensive analysis, we examine the UV properties of the Standard Model under extensions of its fermionic sector. On the other hand, considering the compelling evidence of Asymptotic Safety in gravity, we take into account the gravitational effects in the running of gauge and quark Yukawa couplings. Special attention is given to the gravitationally-induced hierarchy in the quark masses.