Introduction to the Ricci Flow, Summer Semester 2022

This course is an introduction to the beautiful and useful topic of the Ricci Flow. This page will contain all the information related to the course.

Course Outline

Moodle (key: hamilton) Please join Moodle as all the communications regarding the course will be done through it.

Lectures: Mondays 9:15-10:45, Tuesdays 11:15-12:45 in Johann von Neumann-Haus - 1.012.

Tutorials: Mondays 11:15-12:45 in Johann von Neumann-Haus - 1.012.

  • 19.04.2022: The Problem Sessions will start from Monday, May 2nd 2022.

Lecture Notes

For some topics (but not all), I'll upload hand-written lecture notes.

Lec. 2, 3 & 4 - Basic Riemannian Geometry

Lec - Basics of the Ricci Flow

Lec - Variation formulas

Lec - Failure of parabolicity of the Ricci Flow

Lec - DeTurck's trick and short-time existence and uniqueness for the Ricci Flow

Lec - Scalar maximum principles

Lec - Tensor maximum principles

Lec - Ricci pinching estimates

Lec - Applications of pinching and gradient estimates

Problem sets

Problem sets will normally be posted here every Tuesday/Wednesday and discussed in the problem session the following week. They will not be collected or graded but it is highly recommended that you try to attempt all the problems. This will be beneficial to your understanding of the course material.

Problem Set 1 (due on 02.05.2022)

Problem Set 2 (due on 09.05.2022) Sol. to Q.3

Problem Set 3 (due on 16.05.2022) Solutions (Thanks to Johannes Hübers for writing partial solutions in Latex.)

Problem Set 4 (due on 23.05.2022) Solutions

Problem Set 5 (due on 30.05.2022) Solutions

Problem Set 6 (due on 27.06.2022)

Problem Set 7 (due on 04.07.2022)