English
Skeins, clusters, and character sheaves
Multi angle
Auteurs : Jordan, David (Auteur de la Conférence)
CIRM (Editeur )
17B37 - Quantum groups and related deformations
58B32 - Geometry of quantum groups
16TXX - Hopf algebras, quantum groups and related topics
13F60 - Cluster algebras
CIRM (Editeur )
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Résumé :
Skein algebras are certain diagrammatically defined algebras spanned by tangles drawn on the cylinder of a surface, with multiplication given by stacking diagrams. Quantum cluster algebras are certain systems of mutually birational quantum tori whose defining relations are encoded in a quiver drawn on the surface. The category of quantum character sheaves is a $q$-deformation of the category of ad-equivariant $D$-modules on the group $G$, expressed through an algebra $D_q (G)$ of “q-difference” operators on $G$.
In this I talk I will explain that these are in fact three sides of the same coin – namely they each arise as different flavors of factorization homology, and hence fit in the framework of four-dimensional topological field theory.
Codes MSC : In this I talk I will explain that these are in fact three sides of the same coin – namely they each arise as different flavors of factorization homology, and hence fit in the framework of four-dimensional topological field theory.
17B37 - Quantum groups and related deformations
58B32 - Geometry of quantum groups
16TXX - Hopf algebras, quantum groups and related topics
13F60 - Cluster algebras
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/04/2019 Date de captation : 02/04/2019 Sous collection : Research talks arXiv category : Quantum Algebra ; Geometric Topology ; Representation Theory Domaine : Algebra ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 01:03:31 Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-02_Jordan.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Symplectic representation theory / Théorie symplectique des représentationsOrganisateurs de la rencontre : Bellamy, Gwyn ; Ben-Zvi, David ; Schedler, Travis ; Schiffmann, Olivier ; Shan, Peng Dates : 01/04/2019 - 05/04/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/1956.html
Données de citation
DOI : 10.24350/CIRM.V.19511303Citer cette vidéo: Jordan, David (2019). Skeins, clusters, and character sheaves. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19511303 URI : http://dx.doi.org/10.24350/CIRM.V.19511303 |
Voir aussi
- [Multi angle] A geometric $R$-matrix for the Hilbert scheme of points on a general surface / Auteur de la Conférence Arbesfeld, Noah.
- [Multi angle] Affine Springer fibers and G1T modules / Auteur de la Conférence Vasserot, Eric.
- [Multi angle] A sheaf theoretic approach towards calculating simple characters of algebraic groups / Auteur de la Conférence Fiebig, Peter.
- [Multi angle] Langlands duality and quantum field theory / Auteur de la Conférence Yoo, Philsang.
- [Multi angle] Mirabolic Satake equivalence / Auteur de la Conférence Ginzburg, Victor.
- [Multi angle] Irreducible equivariant perverse coherent sheaves on affine Grassmannians of type $A$ and dual canonical bases / Auteur de la Conférence Finkelberg, Michael.
- [Multi angle] Higher representations of $gl(1|1)^+$ / Auteur de la Conférence Rouquier, Raphaël.
- [Multi angle] Symplectic singularities and nilpotent orbits / Auteur de la Conférence Namikawa, Yoshinori.
- [Multi angle] Partial resolutions/deformations of diagonal invariants and representations of finite reductive groups / Auteur de la Conférence Bonnafé, Cédric.
- [Multi angle] Schubert calculus and self-dual puzzles / Auteur de la Conférence Halacheva, Iva.
- [Multi angle] Fusion rings from quantum groups and DAHA actions / Auteur de la Conférence Stroppel, Catharina.
- [Multi angle] Quantum character varieties at roots of unity / Auteur de la Conférence Safronov, Pavel.
- [Multi angle] Character stacks and $(q-)$geometric representation theory / Auteur de la Conférence Gunningham, Sam.
- [Multi angle] The partial compactification of the universal centralizer / Auteur de la Conférence Balibanu, Ana.
- [Multi angle] $T$-structures from categorical actions / Auteur de la Conférence Koppensteiner, Clemens.
- [Multi angle] Gelfand-Tsetlin theory and Coulomb branches / Auteur de la Conférence Webster, Ben.
- [Multi angle] BFN Springer theory / Auteur de la Conférence Kamnitzer, Joel.
- [Multi angle] Coulomb branches of quiver gauge theories with symmetrizers / Auteur de la Conférence Nakajima, Hiraku.
Bibliographie
