Gérard Ben Arous, NYU

Complexity of random landscapes (10.5h)

1. An amateur's view of the optimization problems of Data Science and Machine learning

2. Complexity of random functions of many variables: Kac-Rice's formula as a dictionary between random geometry and random matrices

3. Complexity of the Spherical Spin Glasses: a rigorous approach to the TAP picture and temperature chaos

4. Complexity of Spiked Tensor models: the topological transition. The Kac-Rice and the replica pictures

5. Shorter time dynamics for the Spiked Tensor model. Are the critical points important at all?

6. Some mysteries of Stochastic Gradient Descent

7. More realistic landscapes and harder random matrix models, flat directions, and even more trouble