Jeudi 19 Mai

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Jeudi 19 Mai
Heure: 10:15 - 12:00
Lieu: Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Résumé: Topologie algébrique - Distance, strong convexity, flagness, and associahedra -
Description: Lionel PourninOne can always transform a triangulation of a convex polygon into
another by performing a sequence of edge flips, which amounts to follow a
path in the graph G of the associahedron. The least number of flips
required to do so is then a distance in that graph whose estimation is
instrumental in a variety of contexts, as for instance in computational
biology, in computer science, or in algebraic topology. On the other
hand, it is known that paths in G correspond to a certain kind of
3-dimensional triangulation. This talk is about the recent proof that
these 3-dimensional triangulations are flag when the corresponding path
is a geodesic. This result, that provides a new powerful tool to study
the geometry of G, can be thought of as a 3-dimensional analogue of a
well-known strong convexity property of G. Several consequences on the
computation of distances in G and on strong convexity in related graphs
will be discussed. This talk is based on joint work with Zili Wang
(Dartmouth College).