Ricci Flow and the Poincare Conjecture Fall 2019

Instructor: Danny Calegari

Tu-Th 12:30-1:50 Eckhart 203

Description of course:

This course is an introduction to Ricci flow, and the work of Hamilton and Perelman. We aim to explain some of the key ideas, and to sketch the proof of the Poincare Conjecture.

Cancellations:

The class on Tuesday October 15 is cancelled

Notices:

None yet.

Syllabus:

The skeleton of the syllabus is the following.

• Introduction
• Comparison with mean curvature flow
• Evolution and pinching of curvature
• Limits and singularities
• Perelman's monotone functionals
• Surgery
• Finite time extinction
• Collapsing

Notes from class:

Notes from class will be posted online here and updated as we go along (notes updated 10/31/2019).

References:

• B. Kleiner and J. Lott, Notes on Pereleman's Papers
• Perelman, The entropy formula for the Ricci flow and its geometric applications
• Perelman, Ricci flow with surgery on three-manifolds
• Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Tao, Perelman's proof of the Poincare Conjecture