Title	On the Geometric Langlands Conjecture and Non-Abelian Hodge Theory
Creator	Donagi, Ron
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-11-19T09:01
Description	The Geometric Langlands Conjecture (GLC) for a curve \(C\) and a group \(G\) is a non-abelian generalization of the relation between a curve and its Jacobian. It claims the existence of Hecke eigensheaves on the moduli of \(G\)-bundles on \(C\). The parabolic GLC is a further extension to curves with punctures. After explaining and illustrating the conjectures, I will outline an approach to proving them using non-abelian Hodge theory. A key geometric ingredient is the locus of wobbly bundles: bundles that are stable but not very stable. If time allows, I will discuss two instances where this program has been implemented recently: GLC for \(G=GL(2)\) and genus 2 curves (with T. Pantev and C. Simson), and parabolic GLC for \(\mathbb{P}^1\) with marked points (with T. Pantev).
Extent	62.0 minutes
Subject	Mathematics; Algebraic geometry
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Pennsylvania
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2021-01-19
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0395654
URI	http://hdl.handle.net/2429/77143
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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On the Geometric Langlands Conjecture and Non-Abelian Hodge Theory Donagi, Ron

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