Explores Sum of Squares polynomials and Semidefinite Programming in Polynomial Optimization, enabling the approximation of non-convex polynomials with convex SDP.
Covers Markov Chain Monte Carlo for sampling high-dimensional distributions, discussing challenges, advantages, and applications like the Knapsack Problem and cryptography.
Delves into deep learning's dimensionality, data representation, and performance in classifying large-dimensional data, exploring the curse of dimensionality and the neural tangent kernel.