Lectures related to Exercise machine

Explores convergence in law, weak convergence, and Skorokhod's representation theorem in probability theory.

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Discusses defining tensors, space-time dimensionality, and challenges in formulating a relativistic theory of gravity.

Covers Sobolev spaces, Lax-Milgram theorem, embeddings, and Lipschitz boundaries in PDEs.

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.

Covers quantum wire analysis, transmission function, and tunneling in dots.