Geometry Lecture (10h) Analysis on manifolds

Jérôme Bertrand

• Lecture 1 (2 hours) Manifolds with boundary, Bishop inequality, Laplacian of the distance function.
• Lecture 2 (2 hours) Differential operators and their formal adjoints, the Hodge-de Rham theorem. Basic spectral geometry.
• Lecture 3 (2 hours) Some examples of Spectra, The minimax principle.
• Lecture 4 (2 hours) Eigenvalues estimates, Bishop’s theorem, Lower bounds for the first eigenvalue.
• Lecture 5 (2 hours) Paul Levy’s isoperimetric inequality

Statistics Lecture (10h)  Statistical Learning

Jean-Michel Loubes and Laurent Risser

• Lecture 1 (2 hours) From linear regression to non linear regression. GLM and other extensions.
• Lecture 2 and 3 (4 hours) Regression trees. Bagging. Boosting.
• Lecture 4 (2 hours) Introduction to deep learning.
• Lecture 5 (2 or 4 hours) Stochastic gradient for online learning