Ricci Flow and Geometrization

Abstract: In this general talk, I will give a brief and non-technical tour on role of analysis in studying problems in geometry as well as some other mathematical branches. This can be done through Ricci flow and geometrization. Geometrization is to equip manifolds under consideration a useful metric structure, such a metric structure is often given by the Einstein equation.

An effective method of achieving geometrization is to use Ricci flow introduced in early 80s. Since then, it has had many applications. The most famous one is Perelman’s solution of the Poincare conjecture. In this talk, I will first start with some basics on metrics and explain how geometrization determines topology of surfaces. Then I will introduce Ricci flow and show some of their properties.

I will discuss how Ricci flow is applied to geometrization of surfaces and its generalization to higher dimensions. One deep application in higher dimensions is to solve Thurston’s geometrization conjecture for 3-manifolds, particularly, the Poincare conjecture. The other is the Analytic Minimum Model Program which aims at classifying Kahler manifolds birationally. Some open questions may be presented in the end.

Mathematics

Audience: researchers in the discipline

( slides | video )

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ITB Mathematics Distinguished Lecture Series

Series comments: We aim to bring prominent mathematicians exploring the role of mathematics from various fields, in an intriguing style. The online lectures address quite broad audience, from mathematics students (advanced undergraduate to graduate ones), as well as mathematicians in Indonesia, and our neighboring countries, or even beyond our region. With this lecture series we hope to foster and promote research culture, as well as to highlight the prominent role of mathematics in shaping future society.

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