A non-abelian Hodge theorem for twisted vector bundles- Alberto Garcia-Raboso

Conference Title: GEAR Retreat 2012 Theme: Higgs Bundles (3 of 5) Title: A non-abelian Hodge theorem for twisted vector bundles Speaker: Alberto Garcia-Raboso, University of Pennsylvania; Date and Time: Tuesday August 7, 14:00 Description: I will discuss a generalization of the non-abelian Hodge theorem of Corlette and Simpson. This correspondence is built up in two stages. In the first one, abelian Hodge theory relates Gm-gerbes with flat connection over a smooth complex projective variety X to Higgs Gm-gerbes over X. The category of vector bundles on the flat gerbe equipped with a connection compatible with that of the gerbe is then equivalent to the category of appropriately defined Higgs bundles over the corresponding Higgs gerbe. An interesting case of this correspondence is that of locally free twisted D-modules on X in the sense of Beilinson and Bernstein. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Alberto Garcia-Raboso, in this GEAR Retreat 2012 session on Higgs Bundles, will discuss a generalization of the non-abelian Hodge theorem of Corlette and Simpson, in relation to Gm-gerbes and Higgs gerbes.