100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Thierry Gallay

Pengfei Huang

Hodge theory: from abelian to non-abelian
Mercredi, 13 Novembre, 2019 - 17:00 à 18:00
Résumé : 

Roughly speaking, non-abelian Hodge theory is an analogue of abelian Hodge theory by replacing the abelian groups into non-abelian groups, which gives the equivalence between the category of semisimple flat bundles, the category of polystable Higgs bundles with vanishing Chern classes, the cat- egory of polystable λ-flat bundles and that of harmonic bundles, these were built based on the work of Donaldson, Corlette, Hitchin, Simpson, Deligne and Mochizuki.

In this talk, first I will give a brief introduction on the origin of the non- abelian Hodge theory arising from abelian Hodge theory (i.e, the classical Hodge theory), then I will try to introduce these results with more details. If time permits, I will introduce the related topics on non-abelian Hodge theory, especially the twistor space construction.

 

Institution de l'orateur : 
Université de Nice
Thème de recherche : 
Compréhensible
Salle : 
Salle 4
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