Beijing Institute of Mathematical Sciences and Applications

In the second half of Part III of this course series, we looked at some aspects of the foundations (semigroup theory, symmetric/self-adjoint extensions, quadratic forms, and so on), mostly following Professor Baudoin's lecture notes on Dirichlet spaces. This semester we will continue from there to develop necessary foundations leading to the concepts of the heat semigroup and heat kernel. After that we will further study the connections between heat kernels and functional inequalities.