Abstract: The geometric flow of hypersurfaces is an interesting and active area. Its importance lies in the applications in geometry and topology. For example, Huisken and Ilmanen in 2001 applied the inverse mean curvature flow to prove the famous Penrose conjecture. Brendle-Guan-Li proposed a conjecture on the Alexandrov-Fenchel inequalities for hypersurfaces in the sphere and introduced a locally constrained fully nonlinear curvature flow to study this conjecture.  In this talk, we will discuss using a new type of flow to study this question and some recent progress on this conjecture.