Abstract

Recent high-resolution observations of protoplanetary discs have shown that sub-structures like rings, gaps and lopsided features are common in their continuum dust emission. Using molecular lines, the gas kinematics have been shown to display similarly interesting features. One mechanism to explain such signatures is the interaction of one or more planets with their birth environment, driving waves due at resonances and opening gaps in the disc. From a theoretical point of view, gap formation is important to understand as it determines the torque on the planet and affects its ability to excite waves and drive global disc evolution. I will discuss a semi-analytical approach to try and predict the stability of planet-induced gaps with regards to the Rossby-wave instability, that leads to vortex formation. Furthermore, I will give an overview of recent developments in the theory of Type II migration and discuss open questions.