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H 2 Wall-crossing for Donaldson-Thomas invariants

Auteurs : Bridgeland, Tom (Auteur de la Conférence)
CIRM (Editeur )

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wall-crossing iso-Stokes deformations Calabi-Yau categories stability condition Donaldson-Thomas invariants Kontsevich-Soibelman wall-crossing formula Riemann-Hilbert problem questions of the audience

Résumé : There is a very general story, due to Joyce and Kontsevich-Soibelman, which associates to a CY3 (three-dimensional Calabi-Yau) triangulated category equipped with a stability condition some rational numbers called Donaldson-Thomas (DT) invariants. The point I want to emphasise is that the wall-crossing formula, which describes how these numbers change as the stability condition is varied, takes the form of an iso-Stokes condition for a family of connections on the punctured disc, where the structure group is the infinite-dimensional group of symplectic automorphisms of an algebraic torus. I will not assume any knowledge of stability conditions, DT invariants etc.

Codes MSC :
14D20 - Algebraic moduli problems, moduli of vector bundles
14F05 - Sheaves, derived categories of sheaves and related constructions
18E30 - Derived categories, triangulated categories
32G15 - Moduli of Riemann surfaces, Teichmüller theory
81T20 - Quantum field theory on curved space backgrounds

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 24/04/17
    Date de captation : 11/04/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 01:26:09
    Domaine : Algebraic & Complex Geometry ; Mathematical Physics
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-04-11_Bridgeland.mp4

Informations sur la rencontre

Nom du congrès : Hodge theory, Stokes phenomenon and applications / Théorie de Hodge, phénomène de Stokes et applications
Organisteurs Congrès : Hertling, Claus ; Sabbah, Claude ; Sevenheck, Christian
Dates : 10/04/17 - 14/04/17
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1585.html

Citation Data

DOI : 10.24350/CIRM.V.19158403
Cite this video as: Bridgeland, Tom (2017). Wall-crossing for Donaldson-Thomas invariants. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19158403
URI : http://dx.doi.org/10.24350/CIRM.V.19158403

Voir aussi

Bibliographie

  1. Bridgeland, T. (2017). Riemann-Hilbert problems from Donaldson-Thomas theory. - https://arxiv.org/abs/1611.03697

  2. Bridgeland, T. (2016). Hall algebras and Donaldson-Thomas invariants. - https://arxiv.org/abs/1611.03696

  3. Bridgeland, T., & Toledano-Laredo, V. (2011). Stability conditions and Stokes factors. - https://arxiv.org/abs/0801.3974



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