报告题目：W-entropy formula on super Ricci flow and optimal transport, from Perelman to Lott-Villani

报 告 人：李向东研究员（中科院数学与系统科学研究院）;

报告时间：2016年1月19日15:30

报告地点：知新楼B1238

摘要：Inspired by G. Perelman's work for the proof of Poincare's conjecture, we prove the W-entropy formula for the heat equation of the time dependent Witten Laplacian on super Ricci flow. We then prove the W-entropy formula for the transport equation and the Hamilton-Jacobi equation on manifolds. Our work recaptures Lott-Villani's theorem on the displacement convexity of the Boltzmann type entropy on the Wasserstein space over Riemannian manifolds with non-negative Ricci curvature. To better understand the above two results, we introduce the Langevin deformation of flows on the Wasserstein space, which interpolates the heat equation and the Hamilton-Jacobi equation on manifolds. The W-entropy formula is extended to this deformation. Joint work with Songzi Li.

欢迎各位老师同学积极参加！