15:30-16:30, Seminar Hall
A Hitchin-Kobayashi correspondence for pseudo-real twisted Higgs pairs
Luis Angel Calvo
ICMAT, Madrid.
08-12-17

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Abstract

Sir M. Atiyah introduced in 60's the notion of real vector bundle over a Klein surface. In the later years, there has been a great development in the theory that has been extended to principal bundles and Higgs bundles. A twisted Higgs pair is an object that generalize Higgs bundles, it consists of a principal bundle and a section of an associated real vector bundle twisted by a fixed line bundle. Some examples are: quadric bundles, triples, coherent systems...I introduce pseudo-real structures for twisted Higgs pairs and give a sketch of the proof of the Hitchin-Kobayashi correspondence between real polystable twisted Higgs pairs and real reductions of the structure group of the principal bundle to the maximal real compact group that are solutions to the Hermite-Einstein equations.