Buondì, Mercoledì prossimo alle 11 si terrà un altro seminario di geometria in Aula Magna. Come sempre, chi vuole partecipare dovrà mandarmi la propria adesione entro le 17 del giorno precedente (se potete, meglio prima possibile). Il seminario verrà trasmesso in diretta e registrato in questo canale Teams: https://teams.microsoft.com/l/channel/19%3a540f44c5cea54ac09f8bb6d267f8cdaf%40thread.tacv2/Generale?groupId=816eb116-bda9-4101-9661-7bf70caf33de&tenantId=c7456b31-a220-47f5-be52-473828670aa1 Nello stesso canale c'è la registrazione del seminario precedente, che rimarrà nella cartella File. Purtroppo per colpa mia nella registrazione manca il pezzo introduttivo iniziale, ma miracolosamente si riesce a seguire lo stesso. Seguono i dati del prossimo seminario. A presto, Bruno 14-Oct-2020 - 11:00 Cusps of Hyperbolic 4-Manifolds and Rational Homology Spheres <http://www.dm.unipi.it/webnew/it/seminari/cusps-hyperbolic-4-manifolds-and-rational-homology-spheres> Leonardo Ferrari By Margulis’ Lemma, a finite-volume complete hyperbolic n-manifold has a finite number of ends called cusps, each of which is diffeomorphic to the product of a flat (n-1)-manifold with the half-line. These flat manifolds are called cusp sections, and their possible configurations on hyperbolic manifolds is still very little understood. For instance, it was still not known if a hyperbolic manifold could have only rational homology spheres as cusp sections. In the 4-dimensional case, of the 10 flat 3-manifold diffeomorphism types, only the Hansche-Wendt manifold is a rational homology sphere, and it was conjectured if there existed an orientable hyperbolic 4-manifold such that all the cusps sections were such a manifold. We will introduce combinatorial tools to build manifolds by gluing copies of polytopes - a technique called colouring - and computational tools to tree-search for manifolds, thus providing an example that answers affirmatively this conjecture. Joint work with Leone Slavich and Sasha Kolpakov.