Lectures related to Conformal Bootstrap: OPE and Ward Identities

Quantization: Topological Operators

Covers the quantization of topological operators and Ising models on square lattices.

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

Operator Product Expansion

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

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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.

Segal CFT: Hilbert Space Applications

Covers the applications of Segal's Conformal Field Theory in Hilbert spaces.

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Radial Quantization & Inner Products

Covers radial quantization and inner products in quantum field theory.

Quantum Mechanics: Mathematical Framework

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Unitary Minimal Models: Representation Theory Insights

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Quantum Chaos and Scrambling

Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Singular Vectors in Liouville CFT: Representation Theory Insights

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Local Fields and Correlations in Ising Models

Covers local fields and correlations in Ising models and conformal field theory.

Conformal Field Theory Basics

Covers the basics of Conformal Field Theory, focusing on Large N CFTs and correlation functions.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Understanding Chaos in Quantum Field Theories

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

Easing Model Conformal Theory: Scaling Limits and Correlations

Covers the Easing model conformal theory, focusing on scaling limits and correlation functions.