English
Higgs bundles for Hecke eigensheaves in rank 2 and genus 2
Multi angle
Auteurs : Simpson, Carlos (Auteur de la Conférence)
CIRM (Editeur )
14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14H60 - Vector bundles on curves and their moduli
14D24 - Geometric Langlands program: algebro-geometric aspects
14J33 - Mirror symmetry
CIRM (Editeur )
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Résumé :
We'll discuss our joint work with Ron Donagi and Tony Pantev on the construction of the Higgs bundles associated to Hecke eigensheaves for the geometric Langlands program in the case of rank 2 local systems on a curve of genus 2 . Recall that the moduli space of bundles in this case has two connected components: $\mathbb{P}^3$ and the intersection of two quadrics in $\mathbb{P}^5$. We look for Higgs bundles on these spaces with parabolic structure and logarithmic poles along the wobbly locus. This leads to the study of the geometry of the wobbly locus and its singularities, and the use of our Dolbeault higher direct image construction for the calculation of Hecke operators.
Keywords : geometric Langlands correspondence; non-abelian Hodge theory; Hitchin fibration; D-modules; Hecke eigensheaf; wobbly locus
Codes MSC : Keywords : geometric Langlands correspondence; non-abelian Hodge theory; Hitchin fibration; D-modules; Hecke eigensheaf; wobbly locus
14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14H60 - Vector bundles on curves and their moduli
14D24 - Geometric Langlands program: algebro-geometric aspects
14J33 - Mirror symmetry
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 13/05/2025 Date de captation : 21/04/2025 Sous collection : Research talks arXiv category : Algebraic Geometry ; High Energy Physics - Theory Domaine : Algebraic & Complex Geometry ; Lie Theory and Generalizations ; Mathematical Physics Format : MP4 (.mp4) - HD Durée : 00:57:51 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-21_Simpson.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Families of Kähler spaces / Familles d'espaces kählériensOrganisateurs de la rencontre : Cadorel, Benoît ; Cao, Junyan ; Deng, Ya ; Floris, Enrica ; Guenancia, Henri Dates : 21/04/2025 - 25/04/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3221.html
Données de citation
DOI : 10.24350/CIRM.V.20343503Citer cette vidéo: Simpson, Carlos (2025). Higgs bundles for Hecke eigensheaves in rank 2 and genus 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20343503 URI : http://dx.doi.org/10.24350/CIRM.V.20343503 |
Voir aussi
- [Multi angle] A counter-example to the log-canonical Beauville-Bogomolov decomposition / Auteur de la Conférence Patakfalvi, Zsolt.
- [Multi angle] Kähler families of Green's functions / Auteur de la Conférence Guedj, Vincent.
- [Multi angle] The Hassett-Keel program in genus 4 / Auteur de la Conférence Devleming, Kristin.
Bibliographie
- DONAGI, Ron, PANTEV, Tony, et SIMPSON, Carlos. Twistor Hecke eigensheaves in genus 2. arXiv preprint arXiv:2403.17045, 2024. - https://doi.org/10.48550/arXiv.2403.17045
- DONAGI, Ron, PANTEV, Tony. Langlands duality for Hitchin systems. Invent. math. 189, 653–735 (2012). - https://doi.org/10.1007/s00222-012-0373-8
- DONAGI, Ron et PANTEV, Tony. Parabolic Hecke eigensheaves. Parabolic Hecke eigensheaves. Astérisque 435, 2022. - https://doi.org/10.24033/ast.1178
- DONAGI, R., PANTEV, T., et SIMPSON, C. Direct images in non Abelian Hodge theory. arXiv preprint arXiv:1612.06388, 2016. - https://doi.org/10.48550/arXiv.1612.06388
- NARASIMHAN, Mudumbai S. et RAMANAN, Sundararaman. Moduli of vector bundles on a compact Riemann surface. Annals of Mathematics, 1969, vol. 89, no 1, p. 14-51. - https://doi.org/10.2307/1970807
- DRINFELD, V. G. Two-dimensional l-adic representations of the fundamental group of a curve over a finite field and automorphic forms on GL (2). American Journal of Mathematics, 1983, vol. 105, no 1, p. 85-114. - https://doi.org/10.2307/2374382
- LAUMON, Gérard. Correspondance de Langlands géométrique pour les corps de fonctions. 1987. - https://doi.org/10.1215/S0012-7094-87-05418-4
- HITCHIN, Nigel. Stable bundles and integrable systems. 1987. - https://doi.org/10.1215/S0012-7094-87-05408-1
- HAUSEL, Tamás et THADDEUS, Michael. Mirror symmetry, Langlands duality, and the Hitchin system. Inventiones mathematicae, 2003, vol. 153, p. 197-229. - https://doi.org/10.1007/s00222-003-0286-7
- KAPUSTIN, Anton et WITTEN, Edward. Electric-magnetic duality and the geometric Langlands program. Communications in Number Theory and Physics, 1(1):1–236, 2007. - https://doi.org/10.4310/CNTP.2007.v1.n1.a1
- MOCHIZUKI, Takuro. Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $ D $-Modules, Part 1. American Mathematical Soc., 2007. - https://doi.org/10.1090/memo/0869
- ARINKIN, D., BERALDO, D., CAMPBELL, J. , CHEN L, FAERGEMAN, J., GAITSGORY, D, LIN, K., RASKIN, S, ROZENBLYUM, N. .Proof of the geometric Langlands conjecture, 2024 (five papers combined) - https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
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