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Groupe de travail Min Max: Marcos Cossarini
Groupe de travail Min Max: Marcos Cossarini
12-Feb-2019 15:00
Age: 217 days





Le groupe de travail Min-max sur les géométries algorithmique, convexe, différentielle, riemannienne et discrètes reprendra le : mardi 12 février 2019 à 15h30 dans la Salle 4B107 du bâtiment Copernic.
Marcos Cossarini lancera cette saison sur le thème "Discrete geometry of surfaces towards the filling area conjecture", voir abstract en dessous.

Vous êtes tous bienvenus. Pour plus d'information, n'hésitez pas à nous contacter (Éric Colin de Verdière, Matthieu Fradelizi, Alfredo Hubard, Laurent Hauswirth or Stéphane Sabourau) ou à consulter perso-math.univ-mlv.fr/<wbr></wbr>users/hauswirth.laurent/<wbr></wbr>MinMax/
The Min-max working group on computational, convex, differential, Riemannian and discrete geometries will resume on Tuesday, the 12th of February at 15:30 in the Copernic building. 

Marcos Cossarini will launch this season on the theme "Discrete geometry of surfaces towards the filling area conjecture", see abstract below.

Everyone is welcome. For more information, do not hesitate to contact any of us (Éric Colin de Verdière, Matthieu Fradelizi,Alfredo Hubard, Laurent Hauswirth or
Stéphane Sabourau) or to consult perso-math.univ-mlv.fr/<wbr></wbr>users/hauswirth.laurent/<wbr></wbr>MinMax/ <http://perso-math.univ-mlv.<wbr></wbr>fr/users/hauswirth.laurent/<wbr></wbr>MinMax/> 

Best regards, the organizers ---

Title:
Discrete geometry of surfaces towards the filling area conjecture
Abstract:
Is the hemisphere a minimal isometric filling of its boundary circle, or can it be replaced by a Riemannian surface of smaller area without reducing the distance between any boundary points? Gromov posed the question and proved the strict minimality of the Euclidean hemisphere among surfaces homeomorphic to a disk. Ivanov considered more general Finsler metrics and proved that the Euclidean hemisphere is still minimal among disks, but there are many other Finsler disks that isometrically fill the circle and have the same area. In this talk I will present a discrete version of the problem: Can a cycle graph of length 2n be filled isometrically with a square-celled combinatorial surface made of less than n(n−1)/2 cells? (The filling is said isometric if the distance between each pair of boundary vertices, measured along the 1-skeleton graph of the filling surface, is not smaller than the distance along the boundary cycle.) This discrete question is equivalent to the continuous problem for self-reverse Finsler metrics, and is related to some known problems and structures including pseudo-line arrangements, minimizing the number of crossings between curves on surfaces, discrete differential forms, posets (including permutations with the Bruhat order), integral polygons, CAT(0) cubical complexes, integer linear programming, electrical networks and plabic graphs.








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