In the first part of the course we will cover regularity theory for second order partial differential equations and Sobolev spaces, talk about regularity properties of nonlinear PDEs. In the second part of the course we will focus on the Ricci flow, which is the example of highly nonlinear PDE system and discuss some of it basic properties, such as the regularity properties of the equation, types of singularities and Ricci solitons.
Some basic knowledge of PDEs