Beijing Institute of Mathematical Sciences and Applications

The temporary plan for this semester is to continue our study of heat kernels from the quadratic form/heat semigroup perspective, with tools centered around families of log Sobolev inequalities. We will follow the book Heat Kernels and Spectral Theory by E. B. Davies. Chapter 4 of Aspects of Sobolev Type Inequalities is in a similar theme (ultracontractivity of the heat semigroup). The previous two semesters had focuses on (localized) Sobolev type inequalities (I); (scale-invariant) Poincare and parabolic Harnack inequalities (II).