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Wall-crossing for Donaldson-Thomas invariants
Post-edited
Authors : Bridgeland, Tom (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
Abstract :
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.
MSC Codes : 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
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 24/04/17 Conference Date : 11/04/17 Subseries : Research talks arXiv category : Algebraic Geometry ; Differential Geometry ; High Energy Physics Mathematical Area(s) : Algebraic & Complex Geometry ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:26:09 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-04-11_Bridgeland.mp4 
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Information on the Event
Event Title : Hodge theory, Stokes phenomenon and applications / Théorie de Hodge, phénomène de Stokes et applicationsEvent Organizers : Hertling, Claus ; Sabbah, Claude ; Sevenheck, Christian Dates : 10/04/17 - 14/04/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1585.html
Citation Data
DOI : 10.24350/CIRM.V.19158403Cite 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 |
See Also
- [Multi angle] On the Riemann-Hilbert correspondence for irregular holonomic D-modules / Author of the conference D'Agnolo, Andrea.
- [Multi angle] Exponential motives / Author of the conference Fresán, Javier.
- [Multi angle] Semi-infinite Hodge structures in noncommutative geometry / Author of the conference Shklyarov, Dmytro.
- [Multi angle] Skeletons and moduli of Stokes torsors / Author of the conference Teyssier, Jean-Baptiste.
Bibliography
- Bridgeland, T. (2017). Riemann-Hilbert problems from Donaldson-Thomas theory.
- Bridgeland, T. (2016). Hall algebras and Donaldson-Thomas invariants.
- Bridgeland, T., & Toledano-Laredo, V. (2011). Stability conditions and Stokes factors.
