Lectures related to Signals: Analysis and Synthesis

Representation Theory: Algebras and Homomorphisms

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

Vector Representation of Signals

Explores the vector representation of signals, orthogonal functions, and Fourier series.

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Carathéodory's Theorem and Dimension Bound

Explores Carathéodory's Theorem and its dimension implications for set representation.

Unitary Minimal Models: Representation Theory Insights

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Structure of Algebras

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

Monster Group: Representation

Explores the Monster group, a sporadic simple group with a unique representation theory.

Static Equilibrium Modeling: Understanding Forces and Structures

Covers static equilibrium modeling, focusing on forces, bars, and their relationships in structures.

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

Machine Learning at the Atomic Scale

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

Introduction to Quantum Mechanics

Introduces quantum mechanics, covering S-matrix, scattering amplitudes, and optical theorem.

Lie Algebras and Representations

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

Women in Engineering: Gender Equality Challenges

Addresses gender equality challenges in engineering, focusing on statistics and solutions for improving women's representation and opportunities in the field.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Ideals and Representations

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

Untitled

AC Circuits: Reactances, Impedance, Rotating Vectors

Explores reactances, impedance, and rotating vectors in AC circuits.