Lectures related to Operator algebra

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

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Explores Ward identities in Quantum Field Theory, emphasizing classical and quantum cases, symmetry generators, and perturbation theory.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Herglotz Representation Theorem

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Functional Calculus: Self-Adjoint Operators

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

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Discrete Signals and Linear Systems

Explores discrete signals, linear systems, categorization examples, and convolution properties in signal processing.

Segal CFT: Hilbert Space Applications

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

Quantum Theory: Canonical Approach

Explores the canonical approach to quantum theory and working in Fourier space.

Vertex Operator Algebras

Covers the basics of Vertex Operator Algebras, including normal ordering, fields, and product fields.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

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.

Spectral Decomposition of Bounded Self-Adjoint Operators

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Functional Analysis I: Closed Operators

Explores closed operators in functional analysis, focusing on completeness, boundedness, and projections in Banach spaces.

Fractal Uncertainty Principle and Spectral Gaps

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

Essential Operators: Spectrum and Resolvent Set

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

Semigroups of Linear Operators

Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.