Mostramos a existência de separatrizes para folheações de codimensão 1 geradas por dois campos de vectores holomorfos comutativos numa vizinhança de (C³,0).

In this talk we will discuss some aspects of Riemannian geometry where the chosen connection has a nonzero three-form as its torsion tensor. We will show how to decompose the curvature tensor for such a connection in four dimensions and mention how this motivates our definition of
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In the final lecture, we give some applications of Higgs bundle theory to the study of the geometry and topology of character varieties for surface groups, via the identification with moduli of Higgs bundles.

A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic bundle and a holomorphic one-form, the Higgs field, with values in a certain associated vector bundle. A theorem of Hitchin and Simpson says that a stable Higgs bundle admits a metric satisfying
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Classical Hodge theory uses harmonic forms as preferred representatives of cohomology classes. A representation of the fundamental group of a Riemann surface gives rise to a corresponding flat bundle. A Theorem of Donaldson and Corlette shows how to find a harmonic metric in this bundle. A flat...

The Gauss map for surfaces M in 3-space is a map from M into a sphere; I will present the analogue for surfaces in 4-space, showing that it will be a map from M into the product of two spheres. I will also discuss a geometric characterization of Lagrangean surfaces in terms
of their Gauss map.

We review briefly the method of and some important results in geometric quantization, and go on to discuss some of its links with aspects of the geometry of toric manifolds.

Stochastic topology aims at studying "expected" topological properties of random or partially known spaces. Such spaces arise naturally in areas such as shape recognition or in studying configuration spaces of large systems. A different motivation to study the topology of random spaces is the...

In this talk, a proof of a conjecture of B. Shoikhet is presented,
which gives an alternative approach
to deformation quantization in terms of generators and relations: the
proof relies on a recent formality
result in the presence of two branes (or submanifolds).

Lie groupoids are natural generalizations of Lie groups. In the world of Lie groups it is well-known how different fundamental cohomology theories (de Rham cohomology, group cohomology, Lie algebra cohomology) are related. I will outline these relations as well as a consequence regarding the...