Second Week 8-12 July

 

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
 
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