Lectures related to Operator theory

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Traces: Definition and Properties

Explores the definition and properties of traces in functional analysis, emphasizing uniqueness and linear operators.

Segal CFT: Hilbert Space Applications

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

Linear Algebra: Unitary Operators

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Compositions and adjoints of unbounded operators

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Light-ray Operators: Generalization and Applications

Covers light-ray operators in conformal field theory and their properties, including the Null Energy Condition and connections to Lorentz inversion formulas.

Eigenvalue problem: Eigenbasis, Spectral theorem

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Functional Calculus: Self-Adjoint Operators

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.

Discrete Symmetries Introduction

Introduces discrete symmetries, operators, and tetraquarks in quantum field theory.

Fractal Uncertainty Principle and Spectral Gaps

Explores the Fractal Uncertainty Principle, transfer operators, spectral properties, and adapted operators.

Comparing Tangent Vectors: Parallel Transport

Explores parallel transport along loops and covariant derivatives induced by metrics.

Spectral Decomposition of Unbounded Operators

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Quantum Physics I

Explores quantum state evolution, unitary operators, Heisenberg representation, spin precession, and observable averages.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Common Orthonormal Eigenbasis to Normal Commuting Operators

Discusses the existence of a common orthonormal eigenbasis to normal operators.

Wigner Theorem & Time Inversion

Explores the Wigner theorem and time inversion in group theory.

Wigner Theorem; Translation Symmetry

Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.

Transient and Spatial Flow Instabilities

Explores transient and spatial growth in flow instabilities, dispersion relations, and necessary conditions for instability.

Order finding algorithm

Explores the order finding algorithm, focusing on efficiently finding the period modulo N using Quantum Phase Estimation and C-U gates.