Research

Toric manifolds with small Picard number

This research focuses on toric manifolds, which correspond to complete nonsingular fans in the n-real space. In particular, we use the wedge operation on simplicial complexes to study toric manifolds with small Picard number, that is, whose associated fans have only slightly more rays than their dimension.

Set theoretic operads

The purpose of operads is to encode universally all the operations acting on any category of algebras.
I study operads on sets and how they behave with respect to different set theoretic operations with a specific focus on operads on simplicial complexes.
In fact, they appear in the theory of polyhedral products, which for instance helps building topological models for toric manifolds.