Research

My current research interests are at the intersection of combinatorics, geometry and algebra. In particular:

  • the combinatorics of posets, polytopes and matroids;
  • toric varieties;
  • nonlinear algebra;
  • algebraic statistics.
Preprint 2026

Stellahedral geometry of partially ordered sets

Tommaso Faustini, Luis Ferroni, and Ludovico Piazza

arXiv:2609.22078

Construction of the stellahedron from the dual stellahedral transform of a simplex, up to polar duality.
From a simplex to the stellahedron
In preparation 2026

MLdegrees of 3D polytopes with MLdegree one faces

Eliana Duarte, Federico Lazzeri, Bowen Li, Ludovico Piazza, Bernhard Reinke, and Nico Wolf

Presented at MEGA 2026