AbstractFirst, the concept of entropy in physics and geometry wil be discussed. In particular, Perelman’s W-entropy will bereviewed. Then the relation between entropy and Sobolev inequality and the uniform Sobolev inequality along the Ricci flow due to Rugang Ye will be presented. Some geometric applications such as in the case of Gromov almost flat manifolds will also be presented
Abstract:In recent years the study of K-unstable Fano manifolds atracts people's attention. In this talk I will introduce the geometric quantization of the Kähler-Ricci flow and the associated entropy functional introduced by Weiyong He. The "quantized entropy" coincides with the terminology in the quantum information theory. We also show some convergence results and discuss about the finite-d...