Applications de modèles combinatoires issus de la topologie (HDR Benjamin Audoux)

Benjamin Audoux
I2M, Aix-Marseille Université

Date(s) : 16/02/2018   iCal
15 h 00 min - 16 h 30 min

Soutenance d’Habilitation à Diriger des Recherches (HDR)

Classification d’anneaux plongés dans B^4 à homotopie d’enlacement près, notion de produit pour les codes correcteurs quantiques CSS,…

Membres du jury :
– Michel BOILEAU
– Seiichi KAMADA
– David KOHEL
– Christine LESCOP
– Jean-Pierre TILLICH

Applications of combinatorial models from topology

Along its development, topology set up several combinatorial models, and unexpected applications can emerge from them. They can indeed be developped by their own, and then reused in other context, related to topology or not. In a first part we develop a, so-called welded, combinatorial theory which extend the combinatorics of link diagrams and then use it to classify properly embedded annuli in B4 up to link-homotopy. In a second part, we take advantage of a reformulation of CSS error-correcting quantum codes in terms of chain complexes to define a product notion for these codes and give a criterion which provides a control on the minimum distance of the product of two codes. Then we study several families of codes for which the criterion can be efficiently applied.


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