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Séminaire de topologie, géométrie et algèbre

Univalent foundations and the equivalence principle

Nom de l'orateur: 
Benedikt Ahrens
Etablissement de l'orateur: 
INRIA/ École des Mines de Nantes
Lieu de l'exposé: 
Salle Eole
Date et heure de l'exposé: 
02/06/2016 - 11:00

The "equivalence principle" (EP) says that meaningful statements in mathematics should be invariant under the appropriate notion of equivalence - "sameness" - of the objects under consideration. In set theoretic foundations, the EP is not enforced; e.g., the statement "1 ϵ Nat" is not invariant under isomorphism of sets. In univalent foundations, on the other hand, the equivalence principle has been proved for many mathematical structures. In this introductory talk, I first give an overview of earlier attempts at designing foundations that satisfy some invariance property.

Secondary string topology coproduct: geometric and algebraic constructions

Nom de l'orateur: 
Manuel Rivera
Etablissement de l'orateur: 
( IMRG, Paris)
Lieu de l'exposé: 
Date et heure de l'exposé: 
16/06/2016 - 11:00

I will describe a geometric chain level construction of a secondary coproduct operation on a suitable chain model for the free loop space of a manifold using the theory of De Rham chains. Such coproduct was described at the level of homology by Goresky and Higston using different methods. It is secondary in the sense that arises from a "1-parameter family of chain level intersections". The chain level theory around this secondary operation is useful for describing certain phenomena in symplectic topology and symplectic field theory.

TBA

Nom de l'orateur: 
Christine Lescop (Grenoble)
Etablissement de l'orateur: 
Institut Fourier
Lieu de l'exposé: 
Date et heure de l'exposé: 
10/11/2016 - 11:00