Geometry Lecture (10h)  An Introduction to Riemannian Geometry

Paulo Carrillo Rouse

• Lecture 1 (2 hours) Differentiable manifolds, tangent spaces, vector fields.
• Lecture  2 (2 hours)  Riemannian metrics and Riemannian connections.
• Lecture 3 (2 hours) Geodesics; convex neighbourhoods.
• Lecture  4 (2 hours) Curvature. Ricci and scalar curvature. Tensors on Riemannian manifolds.
• Lecture  5 (2 hours) Jacobi fields. Morse Index theorem.

Statistics Lecture (10h) Probability background for statistical learning

Clément Pellegrini and Thierry Klein

• Lecture 1 and 2 (4 hours) Convergence of random variables, SLLN, CLT Delta method and Slutsky lemma , Gaussian vectors, Classical concentration inequalities.
• Lecture 3 (2 hours) Conditional expectation.
• Lecture 4 (2 hours) Parameter estimation in statistics. Moments methods and maximum likelihood estimation. Confidence sets.
• Lecture 5 (2 or 4 hours) Basic methods in statistical learning. PCA, Regression, k-nearest neighbours algorithm, theoretical study of the rate of convergence of the k-nearest neighbours algorithm.