Lectures related to Adjoint representation

Machine Learning at the Atomic Scale

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Central Results in Hermite Forms

Covers central results in Hermite forms and principal series representations in group theory.

Modeling Introduction

Explores the importance of modeling to understand and control complex systems efficiently.

Heisenberg Groups: Introduction

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

Harmonic Stability Analysis

Explores stability analysis of the 1st harmonic in closed-loop systems and the importance of harmonic conditions for limit cycles.

Difference Equations and Controllers

Covers linear difference equations, controllers, discretization, and approximation techniques.

Poincaré Irreps 2: Little Group and Induced Representation

Explores Poincaré irreducible representations, Little Group, and induced representation in the context of momentum eigenstates.

Hilpot Liegr: Understanding Nilpotent Lie Groups

Explores nilpotent Lie groups, their orbits, and adjoint actions, illustrating simplicity and form.

Correspondence between Heis and Co-adjoint Orbits

Delves into the 1-1 correspondence between Heisenberg groups and co-adjoint orbits, showcasing the relationship between Fleis and the co-adjoint of Heis.

The Adjoint Representation

Introduces the concept of the adjoint representation in Lie algebras.

Exponential Family

Covers the properties of the exponential family and the estimation of parameters.

Group Representation: Definition and Examples

Covers the definition of group representation and examples of equivalent representations.

Proportional Controller: Error and Setpoint Effects

Explains the necessity of error in a proportional controller and the effects of the setpoint.

Risk Analysis and Management: Principles II

Covers risk analysis principles, terminology, and quantification methods in engineering.

Cramer's Rule and Matrix Inverse

Covers Cramer's Rule for solving linear equations and calculating matrix inverses.

Cramer's Rule and Matrix Inverse

Explores Cramer's Rule for solving linear equations and calculating matrix inverses.

Linear Maps and the Duality Principle in Mathematics

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

Information Representation: Computation Module

Explores the representation of information, rounding errors, and image encoding.

Relative Homotopy Groups

Covers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.

QED: Gauge Theories

Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.