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Matemática

Difference hierarchies

Por Jean-Éric Pin (Institut de Recherche en Informatique Fondamentale, CNRS et University Paris-Diderot).

Abstract: Difference hierarchies were originally introduced by Hausdorff and they play an important role in descriptive set theory. In this lecture, I will review standard techniques on difference hierarchies, mostly due to Hausdorff. These techniques will be illustrated by some decidability results on difference hierarchies based on shuffle ideals and polynomials of group languages.

"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.

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