Contents/conteúdo

Mathematics Department Técnico Técnico

Colloquium  RSS

23/07/2013, 16:00 — 17:00 — Room P3.10, Mathematics Building
Vladimir Voevodsky, Institute for Advanced Study

Univalent Foundations of Mathematics

I will outline the main ideas of the new approach to foundations of practical mathematics which we call univalent foundations. Mathematical objects and their equivalences form sets, groupoids or higher groupoids. According to Grothendieck's idea higher groupoids are the same as homotopy types. Therefore mathematics may be considered as studying homotopy types and structures on them. Homotopy type theories, the underlying formal deduction system of the univalent foundations allows one to reason about such objects directly.

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The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.

Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.