Representation Theory Courses and Certifications

Insights into Mathematics

A New Paradigm for Mathematics and Physics - Diffusion Symmetry

Explores diffusion symmetry as an alternative to group-theoretic symmetry through gas diffusion, graph walks, hypergroups, fusion rule algebras, and character tables.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Michael Penn

Permutation Orbifolds of Vertex Operator Algebras

A seminar talk on permutation orbifolds of vertex operator algebras.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The S3 Character Table - A New Meaning - Diffusion Symmetry

Reinterprets the S3 character table through conjugacy-class fusion, hypergroups, and a geometric graph-theoretic view.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symmetries and Quantum Mechanics: Class Functions and Number of Irreducible Representations - Lecture 7

Explore the fundamental concepts of group representation theory in quantum mechanics, focusing on class functions and irreducible representation enumeration.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symmetries and Quantum Mechanics: Irreducible Representations, Characters, and Schur's Lemma

Delve into advanced quantum mechanics concepts, exploring group representation theory, irreducible representations, characters, and Schur's lemma in theoretical physics applications.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symmetries and Quantum Mechanics - Representation Theory of Groups

Explore group representation theory fundamentals applied to quantum mechanics, covering Wigner's theorem, irreducible representations, and Schur's lemma.

• YouTube
• 9 hours 47 minutes
• Self-Paced
• Free Video

Wrath of Math

Unique Solutions and the Basis Representation Theorem in Number Theory

Explore a viral math meme where a father rejects his son's creative solution, diving into number theory and the Basis Representation Theorem to prove uniqueness.

• YouTube
• 11 minutes
• Self-Paced
• Free Video

Representation Learning - Theory - Lecture 13

Explore the theoretical foundations of representation learning, examining architectural inductive biases and neural network connections to Gaussian processes.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Music Representation and Hierarchies in Computational Music Theory - Class 7

Explores music representation and hierarchical structures through readings and live coding with the music21 toolkit.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symmetries and Quantum Mechanics - Basics, Wigner's Theorem, and Linear Representations of Groups

Explore the fundamental connection between symmetry and quantum mechanics through group representation theory, focusing on Wigner's theorem and its implications for physical systems.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Mathemaniac

Demystifying Spin 1/2 - Math of Quantum Mechanics

Demystifies spin-1/2 by clarifying quantum states, rotations, and the SU(2)/SO(3) representation through Bloch-sphere visualization.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

IISc Bangalore;  NPTEL

Representation Theory of General Linear Lie Algebra

Classifies finite-dimensional irreducible representations of gl_n through highest-weight theory, culminating in the Weyl character formula and tensor-product rules.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course

Representation Theory of Finite Groups

Study how finite groups are represented as linear transformations, with emphasis on irreducible representations, character theory, and symmetric groups.

• Swayam
• 12 weeks
• No Longer Offered
• Free Online Course

Insights into Mathematics

Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235

Explore a novel algebraic approach to SL(2) and SU(2) representation theory, emphasizing central polynumbers and mset arithmetic, with implications for Lie theory and modern physics.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Hypergroup Definition and Five Key Examples - Diffusion Symmetry 4

Explore finite commutative hypergroups through five key examples, including class and character hypergroups, distance-transitive graphs, double cosets, and automorphism orbits. Gain insights for applications in physics and chemistry.

• YouTube
• 34 minutes
• Self-Paced
• Free Video