“Can a topologist talk about volume?”
Martedì 28 Aprile 2026, ore 17:00 - Aula 2AB40 - Francesco Milizia (Università di Bologna)
Abstract
A fundamental concept in geometry is the volume, which quantifies the extension of an object. The first formulas we learn at school are those to compute how big rectangles and triangles are. As mathematicians we have more sophisticated objects, like Riemannian manifolds, whose metric structure allows to compute volumes (and many other things). What can we do if dealing just with a topological manifold, which can be stretched and deformed while remaining exactly the same topologically, and volumes are meaningless? This premise is an excuse to give a basic introduction to the “minimal” and the “simplicial” volume, two invariants introduced by Gromov (80s).
