Lectures related to Aurifeuillean factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Explores the Weierstrass Preparation Theorem for entire functions and the construction of root sequences.

RST Regulator: Theory and Implementation

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

Understanding Chaos in Quantum Field Theories

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

Polynomial Regulator Design

Covers the design of polynomial regulators using the RST method.

Model Categories: Properties and Structures

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Polynomial Factorization over a Field: Eigenvalues

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Completing the Square in Quadratic Polynomials

Demonstrates completing the square in quadratic polynomials for factorization simplification.

Polynomial Factorization: Field Approach

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Examples: Polynomial Factorization

Covers polynomial factorization examples and polynomial division in complex numbers.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Compression: Prediction

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Integration on H_pxH and Arithme

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.

Möbius Transformations: Properties and Applications

By the instructor Malo Jézéquel explores Möbius transformations and bounded distortion in SL(2, R).

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Complex Numbers: Operations and Applications

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

Matrix Determinant: Factorization and Linear Equations

Covers the determinant of a matrix, factorization, and linear equations with infinite solutions.

Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Signals & Systems II: Difference Equations and Inverse Operators

Explores difference equations, impulse response, BIBO stability, and inverse operators in signal processing.