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タイトル	On the Narasimhan-Seshadri correspondence for real and quaternionic vector bundles.
開催日時	2013年6月17日 16：30～17：30
主催者
講演者	Florent Schaffhauser (University of Los Andes)
場所	慶應義塾大学理工学部　14棟733
内容	The Narasimhan-Seshadri theorem establishes a correspondence between stable holomorphic vector bundles over a compact Riemann surface X and irreducible projective unitary representations of the fundamental group of that surface. When X represents an algebraic curve defined over the field of real numbers, there is an induced Galois action on stable holomorphic vector bundles, whose fixed points exhibit remarkable algebraic properties: they are either real or quaternionic holomorphic vector bundles and semi-stable such bundles behave very similarly to semi-stable holomorphic vector bundles. In particular, there is a symplectic description of moduli spaces of semi-stable real and quaternionic vector bundles of fixed topological type, which, under the assumption that X has real points, implies that the Narasimhan-Seshadri map is Galois-equivariant. In this talk, I shall discuss the Narasimhan-Seshadri correspondence in the context of real and quaternionic vector bundles and show how it leads to a simple, differential-geometric proof of the existence of stable algebraic vector bundles that are definable over the field of real numbers.
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