报告题目：W-entropy formula on super Ricci flow and optimal transport, fromPerelman 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'sconjecture, we prove the W-entropy formula for the heat equation of the time dependent Witten Laplacian on superRicci flow. We then prove the W-entropy formula for the transport equation andthe Hamilton-Jacobi equation on manifolds. Our work recaptures Lott-Villani'stheorem on the displacement convexity of the Boltzmann type entropy on theWasserstein space over Riemannian manifolds with non-negative Ricci curvature.To better understand the above two results, we introduce the Langevindeformation of flows on the Wasserstein space, which interpolates the heatequation and  the Hamilton-Jacobiequation on manifolds. The W-entropy formula is extended to this deformation.Joint work with Songzi Li.

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