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 3dimensional triangulation. This talk is about the recent proof that these 3dimensional 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 3dimensional analogue of a wellknown 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). 

