Secrets of the Renormalization Group

<!--HTML--><p>&nbsp;The renormalization group is a core idea of theoretical physics and organizes phenomena by energy scale.&nbsp; Famously, this flow is coarse graining: as one goes to longer distances degrees of freedom are lost.&nbsp; In spite of this monotonicity&nbsp;there are certain quantities, intrinsically linked to general notions of symmetry and anomalies, that are constants of the renormalization group flow.&nbsp; I will review some of these ideas and briefly discuss several recent applications, including results about the behavior of Yang-Mills theory as a function of the theta-angle.</p>