课程题目：Introduction to Einstein Manifolds and the Ricci Flow

授课人:叶如钢 加州大学圣巴巴拉分校

时间：9月6日 （周二）上午10:00-11:40

地点：管理科研楼1518

课程简介：In this course we'll present basic materials on Einstein manifolds and Ricci flow, including part of Hamilton's theory of the Ricci flow and part of Perelman's theory of the Ricci flow, such as the variational theory of Einstein metrics, obstruction to existence of Einstein metrics, short-time existence of the Ricci flow, 2-dimensional Ricci flow, 3-dimensional Ricci flow, blow-up singularities,the entropy functional, non-collapsing of the Ricci flow, the maximum principles and the Harnack inequalities.

The theory of Einstein manifolds and the theory of the Ricci flow have had major advances in recent years, including Perelman's solution of the Poincare conjecture using the Ricci flow. This course is meant to provide foundational knowledge and skills for understanding more advanced work in these fields.

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