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Unimodualr triangulations of lattice polytopes

Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017

September 05, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Francisco Santos Leal (University of Cantabria)
Location: MSRI: Simons Auditorium
  • lattice polytope

  • unimodular triangulation

  • empty simplices

  • terminal singularities

  • dilation

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC


Lattice polytopes (that is, polytopes with integer-coordiante vertices) are important both in Algebraic Geometry (toric geometry, commutative algebra, singularities) and Optimization (integer programming). In particular some attention has been devoted to triangulations of them and, most particularly, to the existence or not of unimodular triangulations for various families of them. In this talk I’ll try to survey what is known about triangulations of lattice polytopes, with an excursion into the classification of low-dimensional empty simplices, that is, lattice simplices with no lattice points other than their vertices. Empty simplices are important since they are the ``building blocks’’ in to which every lattice polytope can be triangulated.


29478?type=thumb Santos Notes 4.7 MB application/pdf Download
Video/Audio Files


H.264 Video 3-Santos.mp4 182 MB video/mp4 rtsp://videos.msri.org/data/000/029/342/original/3-Santos.mp4 Download
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