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Higgs bundles for Hecke eigensheaves in rank 2 and genus 2
Multi angle
Authors : Simpson, Carlos (Author of the conference)
CIRM (Publisher )
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 (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/05/2025 Conference Date : 21/04/2025 Subseries : Research talks arXiv category : Algebraic Geometry ; High Energy Physics - Theory Mathematical Area(s) : Algebraic & Complex Geometry ; Lie Theory and Generalizations ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 00:57:51 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-21_Simpson.mp4 
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Information on the Event
Event Title : Families of Kähler spaces / Familles d'espaces kählériensEvent Organizers : Cadorel, Benoît ; Cao, Junyan ; Deng, Ya ; Floris, Enrica ; Guenancia, Henri Dates : 21/04/2025 - 25/04/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3221.html
Citation Data
DOI : 10.24350/CIRM.V.20343503Cite this video as: 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 |
See Also
- [Multi angle] A counter-example to the log-canonical Beauville-Bogomolov decomposition / Author of the conference Patakfalvi, Zsolt.
- [Multi angle] Kähler families of Green's functions / Author of the conference Guedj, Vincent.
- [Multi angle] The Hassett-Keel program in genus 4 / Author of the conference Devleming, Kristin.
Bibliography
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