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#Vertex Algebra

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Vertex Operator Algebras

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Explore the foundations and applications of vertex algebras, from basic concepts to advanced topics like Heisenberg algebra and permutation orbifolds.
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10 Lesons
5 hours
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Vertex Algebras and Quantum Groups with Big Center

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Explore vertex algebras and quantum groups with large centers, focusing on semisimple Lie algebras and their connections to quantum geometric Langlands correspondence and logarithmic Kazhdan-Lusztig conjecture.
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1 Lesons
51 minutes
On-Demand
Free-Video
CIMPA UCR

Una Introducción a las Álgebras de Vértices y sus Representaciones

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Explora las álgebras de vértices y sus representaciones, adentrándote en conceptos fundamentales y aplicaciones avanzadas en matemáticas teóricas.
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1 Lesons
47 minutes
On-Demand
Free-Video
CIMPA UCR

Representaciones de Álgebras y Física Matemática

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Explora las álgebras de vértices, sus representaciones y conexiones con la física matemática. Aborda resultados recientes, problemas abiertos y reformulaciones en álgebras de Lie.
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1 Lesons
55 minutes
On-Demand
Free-Video
Michael Penn

A Commutative Vertex Algebra

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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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1 Lesons
35 minutes
On-Demand
Free-Video
Michael Penn

The Normally Ordered Product

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Explore the concept of normally ordered product in vertex algebras, its definition, and importance in understanding vertex operator structures.
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1 Lesons
32 minutes
On-Demand
Free-Video
Michael Penn

The Vector Spaces for Vertex Algebras

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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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1 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

A Gentle Description of a Vertex Algebra

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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.
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6 Lesons
31 minutes
On-Demand
Free-Video
Michael Penn

Permutation Orbifolds of Vertex Operator Algebras

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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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1 Lesons
53 minutes
On-Demand
Free-Video
Michael Penn

Some Example Calculations in the Heisenberg Vertex Algebra

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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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1 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

The Genesis of Vertex Algebras

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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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10 Lesons
35 minutes
On-Demand
Free-Video
Michael Penn

Vertex Algebras - The Non-Negative Products

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Explore the structure of non-negative products in vertex algebras, delving into advanced mathematical concepts and their applications in algebraic theory.
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1 Lesons
24 minutes
On-Demand
Free-Video
IMSA

Quivers, Curve Counting, and Fermionic Sums in Topology

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Explore connections between quantum groups, vertex algebras, and quiver representations in topology. Discover how fermionic forms link these areas, shedding new light on enumerative geometry and curve counting.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Symmetric Closed Subsets of Real Affine Root Systems and Regular Su - Short Talk by Irfan Habib

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Explores symmetric closed subsets of real affine root systems and their applications in representation theory, focusing on algebraic and combinatorial methods.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Abelianizations of Lie Algebras by Dynkin Combinatorics

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Explore Dynkin combinatorics to understand abelianizations of Lie algebras, delving into advanced algebraic structures and their representations in modern mathematics.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Representations of Extended Affine Lie Algebras by Senapathi Eswara Rao

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Explore representations of extended affine Lie algebras, delving into advanced algebraic structures and their applications in mathematical physics and quantum field theory.
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1 Lesons
52 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

From Faces of Weyl Polytopes, to Weights and Characters of Highest Weight Modules by Apoorva Khare

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Explore connections between Weyl polytopes, weights, and characters in highest weight modules. Gain insights into algebraic and combinatorial methods in representation theory.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Mystery and Magic of Component Tableaux by Anthony Joseph

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Explore the intricacies of component tableaux in representation theory, uncovering their mysterious properties and magical applications in algebraic structures.
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1 Lesons
58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Composition Tableau and Construction of the Canonical Weierstrass Section

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Explore the composition tableau and canonical Weierstrass section construction in this advanced algebraic geometry lecture by Yasmine Fittouhi, part of a broader program on representation theory.
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1 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Representation Theory in Infinite-Dimensional Algebras

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Explore advanced representation theory concepts in this talk by Deniz Kus, covering algebraic and combinatorial methods in infinite-dimensional Lie algebras and quantum groups.
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1 Lesons
40 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Vertex Algebras and Associated Varieties - Lecture 2

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Explore vertex algebras and associated varieties in this advanced lecture, delving into modern representation theory and its connections to mathematics and physics.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Vertex Algebras and Associated Varieties by Anne Moreau

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Explore vertex algebras and associated varieties in this lecture by Anne Moreau, part of a workshop on modern representation theory for graduate students and researchers.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Vertex Algebras from Divisors on CY Threefolds and Perverse Coherent Extensions - Lecture 4

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Explore vertex algebras associated with divisors on toric Calabi-Yau threefolds through algebraic and geometric constructions, examining their equivalence and implications.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Vertex Algebras from Divisors on CY Threefolds and Perverse Coherent Extensions - Lecture 3

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Explore vertex algebras associated with divisors on toric Calabi-Yau threefolds through algebraic and geometric constructions, examining their equivalence and implications.
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1 Lesons
2 hours 8 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Vertex Algebras from Divisors on CY Threefolds and Perverse Coherent Extensions - Lecture 2

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Explore vertex algebras associated with divisors on toric Calabi-Yau threefolds through algebraic and geometric constructions, examining their equivalence and implications.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Vertex Algebras from Divisors on CY Threefolds and Perverse Coherent Extensions - Lecture 1

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Explore vertex algebras associated with divisors on toric Calabi-Yau threefolds through algebraic and geometric constructions, examining their equivalence and connections to enumerative geometry.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
M-Seminar, Kansas State University

Virasoro Constraints in Sheaf Theory

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Explore Virasoro constraints in sheaf theory, focusing on recent developments and their application to moduli spaces of sheaves using vertex algebra and wall-crossing techniques.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Extension of Bershadsky-Polyakov Type Algebras

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Explore toroidal shifted algebras and deformed W-algebras, focusing on extensions of Bershadsky-Polyakov type algebras in quantum symmetries.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Diagrammatics in Categories - Lecture 4

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Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique. Développez votre compréhension des applications dans divers domaines.
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1 Lesons
52 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Diagrammatics in Categories - Lecture 5

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Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique, en laissant place à la généralisation.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Affine W-algebras - Lecture 5

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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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1 Lesons
45 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Affine W-algebras - Lecture 4

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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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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Affine W-algebras - Lecture 3

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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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1 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Affine W-algebras - Lecture 2

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

Affine W-algebras - Part I

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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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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

W-algebras and Lax Operators - Lecture 5

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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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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

W-algebras and Lax Operators - Lecture 3

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Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures using advanced algebraic techniques.
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1 Lesons
40 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Special Holonomy and Geometric Structures on Complex Manifolds

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Explore vertex algebras derived from the Hull Strominger system in complex manifolds, delving into special holonomy and geometric structures. Gain insights into advanced mathematical concepts and their applications.
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1 Lesons
56 minutes
On-Demand
Free-Video
Galileo Galilei Institute

A Skein Theoretic Approach to CFT Correlators - Part 1 of 3

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Explore complex CFT, vertex algebras, and algebraic structures in this comprehensive lecture on skein theoretic approaches to correlators in conformal field theory.
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19 Lesons
1 hour 53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Modular Tensor Categories, Quantum Groups and Vertex Algebras - Lecture 4

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Explore connections between modular tensor categories, quantum groups, and vertex algebras. Delve into the logarithmic Kazhdan–Lusztig conjecture linking quantum groups and vertex algebras.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Modular Tensor Categories, Quantum Groups and Vertex Algebras - Lecture 1

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Explore modular tensor categories, focusing on nonsemisimple theory. Gain insights into these mathematical structures and their connections to quantum symmetries and algebraic concepts.
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1 Lesons
1 hour 22 minutes
On-Demand
Free-Video
BunG Seminar

Introduction to Vertex Algebras - From Heisenberg to Virasoro Algebras

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Delve into vertex algebras, exploring Heisenberg, Kac-Moody, and Virasoro structures while understanding their connections to affine W-algebras and Zhu algebra fundamentals.
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1 Lesons
1 hour 44 minutes
On-Demand
Free-Video
BunG Seminar

Semi-infinite Cohomology and BRST Complex in W-algebras

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Delve into advanced mathematical concepts of semi-infinite cohomology, exploring W-algebras through BRST resolution and discovering connections to Tate Lie algebra and Zhu's algebra theory.
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1 Lesons
1 hour 53 minutes
On-Demand
Free-Video
BunG Seminar

Chiral and Factorization Algebra - Lecture 25

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Delve into advanced mathematical concepts exploring chiral and factorization algebras, their equivalence, and the relationship with Lie-* algebras, culminating in the Eckmann-Hilton commutativity theorem.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Fields Institute

Twistor Theory and Vertex Algebras

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Explore the intersection of twistor theory and vertex algebras, delving into advanced mathematical concepts and their applications in geometry and physics.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
BunG Seminar

Chiral Algebras and the Feigin-Frenkel Duality at Critical Level

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Delve into advanced mathematical concepts exploring vertex algebras, chiral algebras, and Feigin-Frenkel duality, with applications to geometric Langlands program and factorization algebras.
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1 Lesons
2 hours 3 minutes
On-Demand
Free-Video