Regular subdivisions and triangulations

Abstract: Subdivisions and triangulations of point configurations in R^d are a central topic of polyhedral combinatorics and among them regular subdivisions form a particular family which enjoys special geometric properties.

A subdivision is regular if it can be obtained by taking the lower faces of a lifting of its vertices in one dimension higher. This lifting process was central to improve the best known lower bound on the number of combinatorial types of polytopes (joint work with Arnau Padrol and Francisco Santos). Moreover, it happens that among the set of all subdivisions of a fixed point configuration, the regular ones have a particular topological structure. Indeed, they are in correspondence with the faces of a polytope called the secondary polytope.

Mathematics

Audience: advanced learners

Barcelona Mathematics Informal Seminar (SIMBa)

Series comments: SIMBa is a youth mathematics seminar organized by graduate students of the Barcelona area. It is aimed towards graduate and last course undergraduate students. Our goals are divulging the knowledge from different branches of mathematics for those interested and promote networking between the attendants.

This seminar is backed by the Faculty of Mathematics and Computer Science at Universitat de Barcelona, Faculty of Mathematics and Statistics at Universitat Politècnica de Catalunya, the Department of Mathematics from Universitat Autònoma de Barcelona, CRM, IMUB and BGSMath.