We will introduce the notion of $G$-Higgs bundle and focus in a particular case which gives us much more information, that of $G$ being the isometry group of a Hermitian symmetric space. In that case, Milnor Wood inequality will bound the Toledo invariant, and when $G$ is of tube type as well,...

A survey of our current understanding of smooth 4-manifolds.

In this talk, I will present the theory of homological link
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It has been several attempts to generalize the ordinary commutative algebraic geometry to the noncommutative situation. The main problem in the direct generalization, is the lack of localization of noncommutative $k$-algebras, $k$ algebraically closed. This can only be done for Ore sets, and does...

Trata-se de apresentar uma cohomologia associada a folheações sem nenhuma estrutura diferenciable, e que para folheações diferenciables suficientemente regulares coincida com a cohomologia de de Rham.
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Moduli spaces of polygons have been, since the ’90s, a widely studied example of K¨ahler reduction. The hyperpolygons spaces are the non-compact hyperK¨ahler quotient analogue to polygons spaces.
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We will prove that if M is an n-dimensional smooth compact
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We show how the theory of Higgs bundles can be applied to the study of the following geometric problem: When can a maximal Sp(4,R)-representation of a surface group be deformed to a representation which factors through a proper reductive subgroup of Sp(4,R)?