Lectures related to Möbius Transformations: Properties and Applications

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.

Explores geometric transformations like translation and homothety in the plane.

Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Explores complex number properties, roots, and polynomial equations in the complex plane.

Explores the spectrum of hyperbolic surfaces, focusing on Fuchsian groups and their actions.

Explores stability properties and fixed points in discrete time solutions.

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

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

Explores reflections in the plane with an orthonormal coordinate system and the properties of the reflection transformation.

Explores vector equations, observation points, and normal equations in a plane.

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

Covers the Picard method for solving nonlinear equations using fixed point iteration.

Covers the theory and implementation of RST regulators, focusing on factorization of zeros and matrix writing.

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

Covers polynomial factorization examples and polynomial division in complex numbers.

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Covers the definitions and properties of transformations of the plane.