Lectures related to Supersymmetry: Massless Multiplets and Chiral Multiplets

Supersymmetry: Motivations and Concrete Applications

Explores the motivations and applications of supersymmetry, including string theory and flavor symmetries, culminating in the Coleman-Mandula theorem.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Complement: Monotone Class Theorem

Explains the independence of events and sets in an algebraic context.

Quantum Field Theory: Exercises on QFT1

Covers exercises on ladder operators, Lorentz invariance, Noether charges, and custodial symmetry in quantum field theory.

Integration: more examples and rational functions

Covers antiderivatives, fundamental theorems, integration techniques, and rational functions.

Lie Groups: Representations and Transformations

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

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Supersymmetry: Lecture 4

Discusses supersymmetry gauge, superfields, anomalous terms, and flat directions in 4D space.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Course Evaluation and Algebra

Covers the course evaluation results and an algebraic explanation of employment rate growth.

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Analytical Study of Space

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Approximations in Engineering: Leading Digits and Dominant Balance

Explores the significance of leading digits and dominant balance in engineering approximations, showcasing historical methods like slide rules and their relevance in solving challenging problems.

Beyond the Standard Model: Effective Quantum Field Theory

Explores effective quantum field theory, the Standard Model's precision, and the search for new physics beyond it.

Geometric Examples

Explores geometric examples related to linear applications in algebra.

Geometric Sequences: Recurrence System

Covers geometric sequences and recurrence systems to find sequence terms and patterns.

Trans-series in Quantum Field Theory: SVZ Approach and Applications

Discusses the SVZ sum rules and their application in quantum field theory, focusing on trans-series and non-perturbative corrections.

Vertex Operator Algebras

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

Optimization Problems: Algebra and Trinomial Equations

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.