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Applications of a fundamental exterior differential system

Por Rui Albuquerque (Universidade de Évora).

Abstract: We present a fundamental exterior differential system associated to any given oriented Riemannian manifold of any given dimension. New equations of Riemannian geometry are found. The differential system coincides with the Cartan structural equations in the 2-dimensional case and had recent developments in 3-dimensions. We show several applications in some particular fields of study, such as weak holonomies, Einstein manifolds and hypersurface theory.

Intersection theory in a nearlysmooth complex space

Por Daniel Barlet (Inst. Élie Cartan, Lorraine).

Abstract: We shall explain how the classical intersection theory of cycles in a complex manifold is generalized to an ambient nearly smooth complex space. A key point is the local moving lemma for cycles in a complex manifold. The new phenomenon is the fact that the intersection multiplicity of two integral cycles may be a rational not integral number in this context.

"A Brief History of Geometry” is a overview of the main historical steps of Geometry, from Euclid to Perelman, via Descartes, Gauss, Riemann, Ricci, Poincaré and Einstein… This conference was given by Jean-Pierre Bourguignon (IHES, France) at the Academy of Sciences of Lisbon the November 2nd, 2017, at the invitation of the Centro de Matemática, Aplicações Fundamentais e Investigação Operacional da Faculdade de Ciências da Universidade de Lisboa, Portugal.

Through works by renowned architects such as Antoni Gaudí, Felix Candela and Oscar Niemeyer, this film intends to show the natural way in which the formulas, the geometry of forms and their concretization are intertwined.

Através de obras de arquitetos de renome como  Antoni Gaudí, Felix Candela e Oscar Niemeyer, este filme pretende evidenciar a forma natural como se entrelaçam as fórmulas, a geometria das formas e a sua concretização.

O vídeo insere-se no projeto Geometria Intuitiva e Interativa (GI2). Mais informações em http://www.gi2.pt/ .

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