Résumé : Algebraic shifting, introduced by Kalai in the 80's, is an operator that canonically associates a shifted complex to a given simplicial complex. The advantage of this operator is that it preserves many combinatorial, topological and algebraic properties of the starting complex and in doing so it translates the initial problem to a simpler instance. We show that among such properties is that of area rigidity, a generalization of graph rigidity, and that every triangulation of a surface with small genus is area rigid. For arbitrary surfaces we initiate a statistical study of the behavior of algebraic shifting, and in turn of area rigidity. We show that asymptotically almost surely the algebraic shifting of a random Delaunay triangulation of any given closed Riemannian surface is concentrated in a simplicial complex that depends only on the genus and the number of vertices. This talk is based on joint works with Eran Nevo and Yuval Peled.

Dernière modification : Monday 17 November 2025

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr