Bamler’s new entropy techniques for the Ricci flow and their applications

I will introduce Bamler’s recent works on the entropy of the Ricci flow. His results show how Nash entropy is involved with local geometry. My coauthors and I have applied his method to various geometric problems and obtained several results. These results include: (1) characterization of a Ricci flow with a closed finite-time singularity model, (2) a local Sobolev inequality on Ricci flow, (3) an optimal volume growth estimate for noncollapsed steady Ricci solitons. The new results presented in this talk are joint works with Richard H. Bamler, Pak-Yeung Chan, and Zilu Ma.