This summer school is aimed at Master’s, PhD students and early-career postdoc with a basic knowledge of (Riemannian) manifolds and Lie groups.

The program includes theoretical lectures—typically two each morning—as well as one or two exercise sessions in the afternoon. A written examination will take place during the second week. For the detailed schedule, see below or click here.

The program will conclude with a final discussion on Friday, during which participants will be informed of the results of the written examination and will receive a certificate of attendance, including the final exam grade. In accordance with the regulations of their home institutions, this may be eligible for the recognition of academic credit points.

To support students attending the summer school, here is a selection of recommended readings on the key topics considered prerequisites for our courses:

1. B. O'Neill, Semi-Riemannian geometry. With applications to relativity. Academic Press, 1983:

Chapter 1 (basic notions about manifolds), Chapter 3 (Riemannian metrics, Levi-Civita connection, geodesics, curvature)

2.  J. M. Lee, Introduction to smooth manifolds. Second edition. Springer, 2013:

Chapters 1,2,3 (basic notions about manifolds), Chapters 7,8 (introduction to Lie groups), Chapter 14 (differential forms), Chapter 17 (de Rham cohomology).

It would be also helpful some prior knowledge on complex and Kähler geometry, see for instance:

A. Moroianu, Lectures on Kähler Geometry. Cambridge University Press, 2007: Part 2: Complex and Hermitian geometry. 

In addition to its educational objectives, the summer school provides a space for discussion and exchange, including a poster and short-talk session.

An excursion and a social dinner are planned for Saturday, the 22nd.