Vertex Algebras and Algebraic Curves

Abstract

This is the text of the Bourbaki seminar that I gave on June 24, 2000.

Cited by in corpus (342)

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• TFT construction of RCFT correlators III: Simple currents
• W Symmetry in six dimensions
• Finite vs. affine W-algebras
• Vertex operator algebras, Higgs branches, and modular differential equations
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Logarithmic Conformal Field Theory: Beyond an Introduction
• Gaudin models with irregular singularities
• W-algebras as coset vertex algebras
• Rationality of admissible affine vertex algebras in the category O
• Whittaker modules for the affine Lie algebra $A_1^{(1)}$
• Cosets of affine vertex algebras inside larger structures
• Joseph ideals and lisse minimal W-algebras
• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity
• Surface Operators and Separation of Variables
• Logarithmic CFTs connected with simple Lie algebras
• Supersymmetry of the Chiral de Rham Complex
• Lectures on Wakimoto modules, opers and the center at the critical level
• On Conformal Field Theory and Stochastic Loewner Evolution
• The N=1 triplet vertex operator superalgebras
• String-net models for non-spherical pivotal fusion categories
• On higher order Sugawara operators
• Bilinear equations on Painleve tau functions from CFT
• Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
• Mirror symmetry in two steps: A-I-B
• Duality Defects in $E_8$
• Trialities of $\mathcal{W}$-algebras
• Holomorphic SCFTs with small index
• Duality of subregular W-algebras and principal W-superalgebras
• A quasi-Hopf algebra for the triplet vertex operator algebra
• Loop group actions on categories and Whittaker invariants
• Screening operators for W-algebras
• Perturbed Defects and T-Systems in Conformal Field Theory
• Howe Pairs in the Theory of Vertex Algebras
• Explicit generators in rectangular affine W-algebras of type A
• Quantum geometry of moduli spaces of local systems and representation theory
• The vertex algebras ${\mathcal{R}}^{(p)}$ and ${\mathcal{V}}^{(p)}$
• On the triplet vertex algebra W(p)
• Instanton moduli spaces and $\mathcal{W}$-algebras
• Classification of supersymmetries
• Twenty-five years of two-dimensional rational conformal field theory
• Invariant theory and the Heisenberg vertex algebra
• Conformal field theory, boundary conditions and applications to string theory
• Conformal Field Theories with Sporadic Group Symmetry
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• A realisation of the Bershadsky--Polyakov algebras and their relaxed modules
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Vertex algebras and quantum master equation
• Universal two-parameter even spin ${\mathcal{W}}_{\infty }$-algebra
• Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction
• Twisted logarithmic modules of vertex algebras
• Rigorous quantum field theory functional integrals over the p-adics I: anomalous dimensions
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• Weight representations of admissible affine vertex algebras
• Quantum Langlands duality of representations of W-algebras
• Bundle Gerbes and Surface Holonomy
• Representation theory of W-algebras, II: Ramond twisted representations
• Non-commutative Hom-Poisson algebras
• Generalized Vertex Algebras
• Building vertex algebras from parts
• The structure of the Kac-Wang-Yan algebra
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Center of the quantum affine vertex algebra in type A
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Fusion rules and complete reducibility of certain modules for affine Lie algebras
• Unitarity of the modular tensor categories associated to unitary vertex operator algebras, I
• Representations of certain non-rational vertex operator algebras of affine type
• Invariant subalgebras of affine vertex algebras
• Poisson vertex algebras in supersymmetric field theories
• Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings
• Higher order loop equations for A_r and D_r quiver matrix models
• Non-local conserved charges from defects in perturbed conformal field theory
• Higher Airy structures and topological recursion for singular spectral curves
• Homotopy Batalin-Vilkovisky algebras
• One-dimensional Chern-Simons theory and the $\hat{A}$ genus
• Conformal blocks from vertex algebras and their connections on ${\overline{\mathcal{M}}}_{g,n}$
• Jet schemes and invariant theory
• Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations
• Chiral differential operators via Batalin-Vilkovisky quantization
• Realizations of the three point algebra $\mathfrak{sl}(2,\mathcal{R})\oplus \left({\Omega }_{\mathcal{R}}/d\mathcal{R}\right)$
• On the Hochschild cohomologies of associative conformal algebras with a finite faithful representation
• Universal enveloping Poisson conformal algebras
• Vortices and Jacobian varieties
• Opers versus nonabelian Hodge
• Arc spaces and the vertex algebra commutant problem
• An operadic approach to vertex algebra and Poisson vertex algebra cohomology
• The PBW Filtration, Demazure Modules and Toroidal Current Algebras
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• On Connections of Conformal Field Theory and Stochastic Lœwner Evolution
• Quasiclassical Lian-Zuckerman Homotopy Algebras, Courant Algebroids and Gauge Theory
• Plethystic Vertex Operators and Boson-Fermion Correspondences
• Cyclotomic Gaudin models: construction and Bethe ansatz
• Super Quantum Airy Structures
• Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Genera of Vertex Operator Algebras and three dimensional Topological Quantum Field Theories
• W-algebras at the critical level
• Singular support of a vertex algebra and the arc space of its associated scheme
• The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for $\widehat{\mathfrak{gl}}(m|n)$
• Continuous homomorphisms between algebras of iterated Laurent series over a ring
• Mirkovic-Vilonen cycles and polytopes
• On the extended Whittaker category
• $\mathcal{W}$-algebras with non-admissible levels and the Deligne exceptional series
• Vertex Lie algebras and cyclotomic coinvariants
• Vertex operators arising from Jacobi-Trudi identities
• Formal Groups, Witt vectors and Free Probability
• Gaudin model and opers
• Supersymmetric W-algebras
• Chiral Homology of elliptic curves and the Zhu algebra
• Orbifolds of lattice vertex algebras under an isometry of order two
• A realization of certain modules for the $N=4$ superconformal algebra and the affine Lie algebra $A_2^{(1)}$
• Supersymmetry and the Suzuki chain
• Higher Airy structures, W algebras and topological recursion
• Subregular W-algebras of type A
• Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules
• On the Ado Theorem for finite Lie conformal algebras with Levi decomposition
• Two-dimensional conformal field theory, full vertex algebra and current-current deformation
• Higher rank isomonodromic deformations and W-algebras
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• 3d Mirror Symmetry and the $\beta \gamma$ VOA
• Rationality of vertex operator algebras
• Structure of Virasoro tensor categories at central charge $13-6p-6p^{-1}$ for integers $p>1$
• The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System
• Lambda: A Mathematica-package for operator product expansions in vertex algebras
• Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT
• Twisted chiral de Rham complex, generalized geometry, and T-duality
• ${\mathrm{H}}^4({\mathrm{Co}}_0;\mathbf{Z})=\mathbf{Z}/24$
• TFT construction of RCFT correlators V: Proof of modular invariance and factorisation
• Opers on the projective line, flag manifolds and Bethe Ansatz
• Vertex algebras and the Landau-Ginzburg/Calabi-Yau correspondence
• W-algebras and Whittaker categories
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Supersymmetric gauge theories, quantisation of moduli spaces of flat connections, and Liouville theory
• Twist-field representations of W-algebras, exact conformal blocks and character identities
• Snapshots of Conformal Field Theory
• Lectures on Elliptic Functions and Modular Forms in Conformal Field Theory
• Zhu's algebras, $C_2$-algebras and abelian radicals
• Convergence of Sewing Conformal Blocks
• Introduction to Vertex Algebras
• Correlation functions and quantum measures of descendant states
• Quasisymmetric sewing in rigged Teichmueller space
• Cyclotomic Gaudin models with irregular singularities
• Lorentzian 2d CFT from the pAQFT perspective
• Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors
• On the Feigin-Tipunin conjecture
• On the geometry of coset branes
• Unitary representations of a loop ax+b group, Wiener measure and Gamma-function
• Vertex algebras and coordinate rings of semi-infinite flags
• The three-dimensional origin of the classifying algebra
• C_2-cofinite W-algebras and their logarithmic representations
• Localization of free field realizations of affine Lie algebras
• W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras
• Twisted Modules over Vertex Algebras on Algebraic Curves
• Gauging Spacetime Symmetries On The Worldsheet And The Geometric Langlands Program -- II
• Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras
• The 3-point Virasoro algebra and its action on a Fock space
• Topological and conformal field theory as Frobenius algebras
• Lectures on perverse sheaves on instanton moduli spaces
• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• Vertex algebras and Teichmüller modular forms
• Center of the quantum affine vertex algebra associated with trigonometric R-matrix
• Conformal invariance and rationality in an even dimensional quantum field theory
• A remark on the $C_2$-cofiniteness condition on vertex algebras
• The Global Geometry of Stochastic Lœwner Evolutions
• Algebro-Geometric Solutions of the Generalized Virasoro Constraints
• The Vertex Algebra $M(1{)}^{+}$ and Certain Affine Vertex Algebras of Level -1
• Hopf algebras and finite tensor categories in conformal field theory
• The algebra of $S{L}_3(\mathbb{C})$ conformal blocks
• CFTs on Riemann Surfaces of genus $g\ge 1$
• Universal factorization spaces and algebras
• Hilbert schemes and W algebras
• Solving loop equations by Hitchin systems via holography in large-N QCD_4
• On duality and extended chiral symmetry in the SL(2,R) WZW model
• Ward identities in the ${\mathfrak{sl}}_3$ Toda conformal field theory
• Representation theory of $L_k\left(\mathfrak{osp}(1|2)\right)$ from vertex tensor categories and Jacobi forms
• Chiral Koszul duality
• Towards Vertex Algebras of Krichever-Novikov Type, Part I
• Beilinson-Drinfeld Schubert varieties and global Demazure modules
• Differential equations, duality and modular invariance
• Enumerative invariants and wall-crossing formulae in abelian categories
• Wall-crossings and a categorification of $K$-theory stable bases of the Springer resolution
• Foliation of a space associated to vertex operator algebra
• Quantum Field Theories on Algebraic Curves. I. Additive bosons
• Flatland: abelian extensions of the Standard Model with semi-simple completions
• The Witten genus and vertex algebras
• On the coadjoint Virasoro action
• Strong generators of the subregular W-algebra and combinatorial description at critical level
• Twisted logarithmic modules of lattice vertex algebras
• W-Symmetry of the Adelic Grassmannian
• Theta Functions and Szegö Kernels
• Gauging Spacetime Symmetries on the Worldsheet and the Geometric Langlands Program
• Vertex operator algebras associated to modified regular representations of affine Lie algebras
• Extending Representations of sl(2) to Witt and Virasoro algebras
• Full vertex algebra and bootstrap -- consistency of four point functions in 2d CFT
• Reduction by stages for finite W-algebras
• Simplicity of higher rank triplet W-algebras
• On Miura maps for W-superalgebras
• Universal structures in $\mathbb{C}$-linear enumerative invariant theories
• On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras
• Center at the critical level for centralizers in type $A$
• Full Logarithmic Conformal Field theory - an Attempt at a Status Report
• On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebra
• Schramm-Loewner evolution with Lie superalgebra symmetry
• Twisted logarithmic modules of free field algebras
• QFT, RG, and all that, for mathematicians, in eleven pages
• Vertex Operators, Grassmannians, and Hilbert Schemes
• Quantum Group as Semi-infinite Cohomology
• Any flat bundle on a punctured disc has an oper structure
• Representation Theory of Superconformal Algebras and the Kac-Roan-Wakimoto Conjecture
• Explicit description of twisted Wakimoto realizations of affine Lie algebras
• On 'categories' of quantum field theories
• G-structures and Superstrings from the Worldsheet
• A generalization of twisted modules over vertex algebras
• Schramm--Loewner-evolution-type growth processes corresponding to Wess--Zumino--Witten theories
• One example of a chiral Lie group
• Equivariant localization in factorization homology and applications in mathematical physics I: Foundations
• Lie algebra automorphisms in conformal field theory
• An algebro-geometric construction of lower central series of associative algebras
• On the continuous series for affine sl(2,R)
• Geometric Langlands for hypergeometric sheaves
• Representations of Twisted Toroidal Lie Algebras from Twisted Modules over Vertex Algebras
• Affine Kac-Moody algebras, integrable systems and their deformations
• Quasimodular moonshine and arithmetic connections
• Affine Demazure modules and $T$-fixed point subschemes in the affine Grassmannian
• A quantization of the Hitchin hamiltonian system and the Beilinson-Drinfeld isomorphism
• Derived gluing construction of chiral algebras
• Uniqueness of open/closed rational CFT with given algebra of open states
• Irregular Wakimoto modules and the Casimir connection
• Coset Vertex Operator Algebras and $\W$-Algebras
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra
• Quantum Group $G{L}_q(2)$ and Quantum Laplace Operator via Semi-infinite Cohomology
• Simple superelliptic Lie algebras
• $N$-point Virasoro Algebras and Their Modules of Densities
• Vertex operators, solvable lattice models and metaplectic Whittaker functions
• Affine opers and conformal affine Toda
• A classification of irreducible Wakimoto modules for the affine Lie algebra $A_1^{(1)}$
• Hom-alternative modules and Hom-Poisson comodules
• A mathematical formalism for the Kondo effect in WZW branes
• DT invariants from vertex algebras
• Equivariant localization in factorization homology and applications in mathematical physics II: Gauge theory applications
• Logarithmic Vertex Algebras
• Bosonizations of ${\widehat{\mathfrak{sl}}}_2$ and Integrable Hierarchies
• Chiral de Rham Complex and Orbifolds
• Invariant subalgebras of the small $\mathcal{N}=4$ superconformal algebra
• Arithmetic partial differential equations
• Localization for affine $W$-algebras
• Vertex operator algebras associated to modified regular representations of the Virasoro algebra
• Lattices, Vertex Algebras and Modular Categories
• Cosets from equivariant W-algebras
• $W$-algebras associated with centralizers in type $A$
• Discrete torsion, orbifold elliptic genera, and the chiral de Rham complex
• A Lie conformal algebra of Block type
• T-duality and the exotic chiral de Rham complex
• Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi-Yau 4-folds
• The quantum group dual of the first-row subcategory for the generic Virasoro VOA
• Automorphic gluing functor in Betti Geometric Langlands
• Vertex algebras and the formal loop space
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• Representations of $a_{\infty }$ and $d_{\infty }$ with central charge 1 on the single neutral fermion Fock space $F^{\otimes \frac{1}{2}}$
• Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions
• A projection formula for the ind-Grassmannian
• $(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated modules for vertex algebras
• Structures of BiHom-Poisson algebras
• A note on the affine vertex algebra associated to $\mathfrak{gl}(1|1)$ at the critical level and its generalizations
• Virasoro action on Imaginary Verma modules and the operator form of the KZ-equation
• Quasi-coherent sheaves in differential geometry
• The varieties of semi-conformal vectors of affine vertex operator algebras
• Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles
• Hopf and Frobenius algebras in conformal field theory
• Unital associative pseudoalgebras and their representations
• Extension of vertex operator algebra $V_{{\hat{H}}_4}(\ell ,0)$
• A chiral Borel-Weil-Bott theorem
• Wakimoto Modules for Twisted Affine Lie Algebras
• Vertex Poisson algebras associated with Courant algebroids and their deformations; I
• Two dimensional current algebras and affine fusion product
• Vertex (Lie) algebras in higher dimensions
• Non-linear Lie conformal algebras with three generators
• BRST Reduction of the chiral Hecke Algebra
• A smash product construction of nonlocal vertex algebras
• Magnetic monopoles on manifolds with boundary
• Classification of operator algebraic conformal field theories in dimensions one and two
• Self-extensions of Verma modules and differential forms on opers
• Quantized Reductions and Irreducible Representations of W-Algebras
• $K$-theory associated to vertex operator algebras
• Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II
• Twisted vertex operators and Bernoulli polynomials
• Orbifold conformal blocks and the stack of pointed G-covers
• Casimir Operators and Monodromy Representations of Generalised Braid Groups
• Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. I
• Topologizations of Chiral Representations
• Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry
• Note on Schramm-Loewner evolution for superconformal algebras
• On certain vertex algebras and their modules associated with vertex algebroids
• Reconstruction of vertex algebras in even higher dimensions
• Operateurs differentiels globaux sur les courbes elliptiques
• Suzuki functor at the critical level
• Vertex algebras and Hodge structures
• Embeddings of vertex operator algebras associated to orthogonal affine Lie algebras
• Coset construction of Virasoro minimal models and coupling of Wess-Zumino-Witten theory with Schramm-Loewner evolution
• Jet schemes, invariant chiral differential operators, and Howe duality
• Vertex algebras and the class algebras of wreath products
• On principal realization of modules for the affine Lie algebra $A_1^{(1)}$ at the critical level
• Algebras of Non-Local Screenings and Diagonal Nichols Algebras
• Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology
• On the $h$-adic quantum vertex algebras associated with Hecke symmetries
• Vertex Algebroids over Veronese Rings
• Li filtrations of SUSY vertex algebras
• Genus-zero Permutation-twisted Conformal Blocks for Tensor Product Vertex Operator Algebras: The Tensor-factorizable Case
• Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane
• Vertex coalgebras, comodules, cocommutativity and coassociativity
• Vertex Algebras and Commutative Algebras
• A geometric construction of integrable Hamiltonian hierarchies associated with the classical affine W-algebras
• A generalized semi-infinite Hecke equivalence and the local geometric Langlands correspondence
• Twisted modules for vertex algebras associated with vertex algebroids
• The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras
• Vertex Algebras and the Equivariant Lie Algebroid Cohomology
• Quantum Strings and Superstrings
• On deformations and extensions of $\text{Diff}(S^2)$
• Vertex algebras and vertex Poisson algebras
• Functional equations in algebra
• Hecke-Langlands Duality and Witten's Gravitational Moonshine
• Quantum Lichnerowicz - Poisson complex
• Associative algebra twisted bundles over compact topological spaces
• Quantum dimensions and fusion products for irreducible V_Q^s-modules, where s is an isometry of Q with s^2=1
• Jacobi complexes on the Ran space
• Towards the multiplicative behavior of the K-theoretical McKay correspondence
• Strongly Homotopy Chiral Algebroids
• Rational and global forms of certain Chiral Conformal Field Theories; Vertex Algebras I
• $K$-theory of moduli spaces of sheaves and large Grassmannians
• Vertex algebras associated to abelian current algebras
• Picard groups in rational conformal field theory
• Chiral vector bundles
• Riemann Surfaces and Vertex Operator Algebras
• Opers and Theta Functions
• Uniformization of the Moduli Space of Pairs Consisting of a Curve and a Vector Bundle
• Cosimplicial meromorphic functions cohomology on complex manifolds
• Introduction to finite $W$-algebras
• Representations of affine Nappi-Witten algebras
• Krichever-Novikov Vertex Algebras on Compact Riemann Surfaces
• A Geometric Proof of the Feigin-Frenkel Theorem
• H_T Vertex Algebras