30 novembre 2017

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Programme : La rencontre annuelle du GDR Géométrie Noncommutative intitulée « Arbre de Noël 2017 du GDR GNC » aura lieu à Orsay les 30 novembre et 1er décembre. Voici la page web de la rencontre :
https://cyrilhoudayer.com/arbre-de-noel-2017-gdr-gnc/

 

Andrei Shafarevich (Moscow State University)
Laplacians and wave equations on polyhedral surfaces

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Lieu : Salle 121-123, bâtiment 425

Résumé : Differential operators on polyhedral surfaces are intensively studied during last decades. Many papers are devoted to such topics as spectral theory, determinants, trace formulas etc. Nice properties of such operators are due to the fact that polyhedra are almost everywhere flat ; on the other hand, there appear interesting effects caused by the singularities (vertices). In the talk, we present some results concerning various properties of Laplacians and the behavior of solutions to wave equations on polyhedral surfaces.

Laplacians and wave equations on polyhedral surfaces  Version PDF

Sigurður Stefánsson (University of Iceland)
Random outerplanar maps and stable looptrees

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Lieu : salle 117/119 du bâtiment 425

Résumé : An outerplanar map is a drawing of a planar graph in the sphere which has the property that there is a face in the map such that all the vertices lie on the boundary of that face. A random outerplanar map is defined by assigning non-negative weights to each face of a map. Caraceni showed that uniform outerplanar maps (all weights equal to 1) with an appropriately rescaled graph distance converge to Aldous’ Brownian tree in the Gromov-Hausdorff sense. This result was generalized by Stufler who showed that the same holds under some moment conditions. I show, in joint work with Stufler, that for certain choices of weights the maps converge towards the alpha-stable looptree, which was recently introduced by Curien and Kortchemski. Our approach relies on the fact that outerplanar maps may be viewed as trees in which each vertex is a dissection of a polygon. Dissections of polygons are further in bijection with trees which allows us to relate the random outerplanar maps to the model of simply generated trees which is understood in detail.

Random outerplanar maps and stable looptrees  Version PDF

Youcef Mammeri (LAMFA, Université de Picardie)
Du phloème au paysage

Jussi Behrndt (TU Graz)
Selfadjoint realizations of the Laplacian on bounded Lipschitz domains

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Lieu : Bât 425, salle 113-115

Résumé : In this talk we discuss the selfadjoint realizations of the Laplacian on bounded Lipschitz domains with the help of Dirichlet and Neumann boundary conditions. One of the key difficulties is to establish the existence and the mapping properties of the Dirichlet and Neumann trace map on the domain of the maximal operator. We pay special attention to Robin type boundary conditions and we also discuss less standard realizations of the Laplacian, as e.g. the Krein-von Neumann extension and its spectral asymptotics.
This talk is based on joint work with Fritz Gesztesy and Marius Mitrea.

Selfadjoint realizations of the Laplacian on bounded Lipschitz domains  Version PDF