Lectures related to Conformal Applications: Theory and Examples

Explores conformal transformations, including holomorphic functions and Moebius transformations.

Conformal Transformations: Theory and Applications

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

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Lecture 5: Conformal Transformations

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Isometries: Transformations Preserving Distances in the Plane

Introduces isometries as transformations preserving distances in the plane, focusing on symmetry and geometric relationships.

Orthogonal Matrices and Eigenvalues

Explores orthogonal matrices, eigenvalues, and orientation-preserving transformations in linear algebra.

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Linear Algebra: Subspaces and Transformations

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

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Holomorphic Functions: Cauchy-Riemann Equations and Applications

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

Complex Analysis: Holomorphic Functions and Cauchy-Riemann Equations

Introduces complex analysis, focusing on holomorphic functions and the Cauchy-Riemann equations.

Translations and Homotheties

Explores translations and homotheties, discussing their properties and practical applications in preserving geometric characteristics.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Linear Algebra Fundamentals

Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.