Lectures related to Von Neumann algebra

Proof of Schmidt Theorem and Entropy Properties

Covers the proof of the Schmidt theorem and properties of von Neumann entropy, including dense coding and entanglement.

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

Explores the Stone-von Neumann Theorem and unitary operators on Hilbert spaces.

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.

Wave Equations Stability

Explores resonant shallow water equations, stability analysis, eigenmodes, and clean modes in waves.

Quantum Information Principles

Covers the mathematical principles of quantum physics, including Hilbert spaces and quantum bits.

Abstract algebra and type classes

Covers abstract algebra concepts using type classes in Scala, including defining monoids, generalizing reduce functions, and typeclass laws.

Hubbard Models: Density Matrix Formalism

Covers the Hubbard models and density matrix formalism in quantum mechanics.

Wave Equation Stability

Explores the stability of the wave equation finite difference scheme and resonant excitation.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

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

Advection-Diffusion: Properties and Stability Analysis

Discusses the properties and stability analysis of advection-diffusion equations and the introduction of explicit finite difference schemes.

Spectral Theory: Friedrichs Extension Theorem

Covers the proof of Friedrichs extension theorem and the properties of the spectrum and resolvent map.

Symmetry in Functions: Definitions and Examples

Explores the definition of pantéch functions and symmetry in functions, including even and odd functions.

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.

Heisenberg Groups: Introduction

Introduces the Heisenberg groups, covering representation theory and unique properties.

Lie Algebras and Representations

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Limits in Infinity: Criteria and Examples

Covers the concept of limits at infinity and discusses criteria and examples of functions approaching infinity.

Advection-Diffusion Equations

Explores numerical solutions and stability analysis of advection-diffusion equations, emphasizing properties of analytical solutions and their behavior over time.