English
Localization and virtual localization, with applications to quadratic curve counts and DT invariants
Multi angle
Auteurs : Levine, Marc (Auteur de la Conférence)
CIRM (Editeur )
14F42 - Motivic cohomology; motivic homotopy theory
14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
19E15 - Algebraic cycles and motivic cohomology (K-theory)
CIRM (Editeur )
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Résumé :
We report on the development of localization methods useful for quadratic enumerative invariants, replacing the classical Gm-action with an action by the normalizer of the diagonal torus in SL2.
We discuss applications to quadratic counts of twisted cubics in hypersurfaces and complete intersections (joint with Sabrina Pauli) as well as work by Anneloes Vierever, and our joint work with Viergever on quadratic DT invariants for Hilbert schemes of points on P3 and on (P1)3.
Keywords : localization; Bott residue formula; quadratic forms; Donaldson-Thomas invariants
Codes MSC : We discuss applications to quadratic counts of twisted cubics in hypersurfaces and complete intersections (joint with Sabrina Pauli) as well as work by Anneloes Vierever, and our joint work with Viergever on quadratic DT invariants for Hilbert schemes of points on P3 and on (P1)3.
Keywords : localization; Bott residue formula; quadratic forms; Donaldson-Thomas invariants
14F42 - Motivic cohomology; motivic homotopy theory
14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
19E15 - Algebraic cycles and motivic cohomology (K-theory)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/11/2024 Date de captation : 04/11/2024 Sous collection : Research talks arXiv category : Algebraic Topology ; Algebraic Geometry Domaine : Algebra ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 01:09:34 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-11-4_Levine.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Motivic homotopy in interaction / Homotopie motivique en interactionOrganisateurs de la rencontre : Déglise, Frédéric ; Dubouloz, Adrien ; Fasel, Jean ; Morel, Sophie ; Østvær, Paul Arne Dates : 04/11/2024 - 08/11/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3129.html
Données de citation
DOI : 10.24350/CIRM.V.20259503Citer cette vidéo: Levine, Marc (2024). Localization and virtual localization, with applications to quadratic curve counts and DT invariants. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20259503 URI : http://dx.doi.org/10.24350/CIRM.V.20259503 |
Voir aussi
- [Multi angle] Cellular A1-homology of smooth algebraic varieties / Auteur de la Conférence Sawant, Anand.
- [Multi angle] What motives know about periods -- and the other way around / Auteur de la Conférence Huber-Klawitter, Annette.
- [Multi angle] Quadratic enumerative invariants and local contributions / Auteur de la Conférence Pauli, Sabrina.
Bibliographie
- LEVINE, Marc. Virtual Localization in equivariant Witt cohomology. arXiv preprint arXiv:2203.15887, 2022. - https://doi.org/10.48550/arXiv.2203.15887
- LEVINE, Marc. Atiyah-Bott localization in equivariant Witt cohomology. arXiv preprint arXiv:2203.13882, 2022. - https://doi.org/10.48550/arXiv.2203.13882
- LEVINE, Marc et PAULI, Sabrina. Quadratic counts of twisted cubics. arXiv preprint arXiv:2206.05729, 2022. - https://doi.org/10.48550/arXiv.2206.05729
- Perspectives on four decades of algebraic geometry Volume 2: in Memory of Alberto Collino, Progress in Mathematics volume 352 (released in 2025) -
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