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Mathematics
Algebra
Vertex Algebra

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Explore the mathematical foundations of vertex algebras, from Heisenberg to Virasoro algebras, through accessible video lectures. Learn fundamental concepts, calculations, and applications to quantum field theory via free YouTube tutorials from leading mathematics research centers and universities.

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Michael Penn
A Gentle Description of a Vertex Algebra

Explore the concept of vertex algebra through associative, Lie, and Poisson algebras. Learn its definition and gain intuition for understanding its components in this mathematical journey.
- YouTube
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Michael Penn
Some Example Calculations in the Heisenberg Vertex Algebra

Explore in-depth calculations within the Heisenberg vertex algebra, demonstrating advanced mathematical concepts and techniques in this specialized field of study.
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Michael Penn
A Commutative Vertex Algebra

Explore the universal commutative vertex algebra with one generator, demonstrating how to give a polynomial ring vertex algebra structure through an in-depth mathematical analysis.
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Michael Penn
Permutation Orbifolds of Vertex Operator Algebras

Explore permutation orbifolds in vertex operator algebras, delving into advanced algebraic structures and their applications in mathematical physics and string theory.
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Michael Penn
The Genesis of Vertex Algebras

Explore the historical development of vertex algebras with Richard Borcherds, covering key concepts like Leech lattice, Dinkin diagrams, and string theory connections.
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Michael Penn
Vertex Algebras - The Non-Negative Products

Explore the structure of non-negative products in vertex algebras, delving into advanced mathematical concepts and their applications in algebraic theory.
- YouTube
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Michael Penn
The Normally Ordered Product

Explore the concept of normally ordered product in vertex algebras, its definition, and importance in understanding vertex operator structures.
- YouTube
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Michael Penn
The Vector Spaces for Vertex Algebras

Explore key vector spaces for vertex algebras: polynomial rings, exterior algebras with infinite variables, and universal enveloping algebra of the Virasoro Lie algebra. Gain essential understanding for advanced algebraic studies.
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Centre de recherches mathématiques - CRM
Extension of Bershadsky-Polyakov Type Algebras

Explore toroidal shifted algebras and deformed W-algebras, focusing on extensions of Bershadsky-Polyakov type algebras in quantum symmetries.
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Centre de recherches mathématiques - CRM
Affine W-algebras - Lecture 5

Explore affine W-algebras construction, theory, and applications in vertex algebra. Delve into quantum Hamiltonian reduction, Virasoro minimal models, and tensor categories of W-algebra representations.
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Centre de recherches mathématiques - CRM
Affine W-algebras - Lecture 4

Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
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Centre de recherches mathématiques - CRM
Affine W-algebras - Lecture 3

Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
- YouTube
- 54 minutes
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Centre de recherches mathématiques - CRM
Affine W-algebras - Lecture 2

Explore affine W-algebras through quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
- YouTube
- 55 minutes
- On-Demand
- Free Video
Centre de recherches mathématiques - CRM
Affine W-algebras - Part I

Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
- YouTube
- 1 hour 4 minutes
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Centre de recherches mathématiques - CRM
W-algebras and Lax Operators - Lecture 5

Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures in quantum algebra and integrable systems.
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