Lectures related to Conformal Transformations: Theory and Applications

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.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Conformal Maps and Hyperbolic Geometry

Explores conformal maps, hyperbolic geometry, and isometric properties of disks.

Conformal Algebra: Transformations and Correlation Functions

Explores conformal algebra, transformations, and correlation functions of primary operators in curved spacetimes.

Conformal Transformations

Explores conformal transformations, scale invariance, and critical points in conformal symmetry.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Quantization: Topological Operators

Covers the quantization process using topological operators and their role in generating symmetries.

Symmetric Inner Products and Conformal Transformations

Covers making inner products symmetric and conformal transformations in local operators computation.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Conformal Transformations

Explores conformal transformations, including holomorphic functions and Moebius transformations.

Quantum Field Theory in AdS: State-Operator Correspondence

Covers the study of free particle quantum mechanics in AdS and the State-Operator Correspondence in AdS.

Conformal Transformations and Stress Tensor

Explores conformal transformations, stress tensor, and correlation functions in conformal field theory.

Conformal Transformations: Symmetries and Correlation Functions

Explores conformal transformations and correlation functions in quantum field theory, emphasizing symmetry preservation and fixed correlation functions.

Statistical Models: Unitary Conformal Field Theories

Covers the connection between statistical models and unitary conformal field theories, focusing on critical points and the role of local fields.

Conformal Field Theory

Covers the basics of Conformal Field Theory, including operators and correlators.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Conformal Correlation Functions

Explores conformal correlation functions, cross-ratios, conformal transformations, algebra, and correlation functions of primary operators.

Weakly Coupled QFT in AdS

Explores weakly coupled quantum field theory in AdS, including state-operator correspondence and semiclassical gravity.

Lie Groups: Representations and Transformations

Explores Lie groups, scalar fields, and vector spaces transformations.