Gabriele Balletti: Connectivity of pseudomanifolds graphs through bounds for the Castelnuovo-Mumford regularity.

While writing my master thesis I came across a nice and simple result which extends some well-known ones (Balinsky-Barnette, Athanasiadis) for the connectivity of 1-skeleta of simplicial pseudomanifolds by weakening the hypotesis; something similar has very recently been achieved in a different way by Adiprasito, Goodarzi and Varbaro. In some extreme cases we will also see that the connectivity may increase exponentially with the dimension of the simplicial complex.