buondi', siete tutti invitati al seminario di geometria di domani, come sempre alle 14.30 in aula seminari. Segnalo anche un workhsop al Centro De Giorgi che inizia domani, dal titolo "Giornate di Geometria Algebrica ed Argomenti Correlati XI": http://crm.sns.it/event/243/ ---- MERCOLEDI' 23 MAGGIO 2012 14:30-15:30, Sala Seminari (Dip. Matematica) SEMINARI DI GEOMETRIA The number of triangulations with N simplices, for N large Bruno Benedetti (KTH, Stockholm) How many triangulations of S^3 are there: exponentially many, or more? This question was asked among others by Gromov, and it has repercussions on physics. The count is usually performed with respect to the number N of facets; two triangulations are considered different if their face posets are not isomorphic. We show that *shellable* triangulations of S^3 are only exponentially many. In particular, there are exponentially many polytopes with N facets. This is joint work with Gunter Ziegler (http://www.springerlink.com/content/x8r6mm1155102542/?MUD=MP). If time permits, we will also sketch some recent progress on this, showing that under some extra `bounded geometry' assumptions (in the sense of Cheeger), one can reach exponential bounds for the number of triangulated d-manifolds with N simplices (for fixed d). Unfortunately, the technical assumption cannot be removed: Already for d=2, there are more than exponentially many surfaces with N triangles. This is joint work with Karim Adiprasito (http://arxiv.org/abs/1107.5789). ----