Francesca Tombari: Less is more

Posets are sets with a partial order defined on them. What can you do with a mathematical object with so little structure? Well, many things! In this talk, we will see two ways to define a notion of dimension in a poset and a construction to transform a discrete poset into a continuous one by filling in its "gaps". If time allows, we will see how to use these ideas in the context of topological data analysis.