Lectures related to Critical Behavior in General Relativity

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.

Covers linear applications, matrices, transformations, and the principle of superposition.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Explores the renormalization group applied to the Ising model and the derivation of the central limit theorem.

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Explores Galilean transformations in spacetime, focusing on measurements and coordinate transformations.

Explores mixing properties of infinite measure preserving systems, focusing on suspensions, Govers transformations, and Lorentz gas.

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers the Newton method for finding zeros of functions using data interpolation.

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.