You are here

Unimodular triangulations of sufficiently large dilations

Gaku Liu, University of Washington
Wednesday, January 25, 2023 - 4:00pm to 5:30pm
PDL C-38 and via Zoom Link:
Gaku Liu
Gaku Liu


An integral polytope is a polytope whose vertices have integer coordinates. A unimodular triangulation of an integral polytope in \$\mathbb R^d\$ is a triangulation in which all simplices are integral with volume \$1/d!\$. A classic result of Kempf, Mumford, and Waterman states that for every integral polytope \$P\$, there exists a positive integer \$c\$ such that \$cP\$ has a unimodular triangulation. We strengthen this result by showing that for every integral polytope \$P\$, there exists \$c\$ such that for every positive integer \$c' \ge c\$, \$c'P\$ admits a unimodular triangulation.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 4:00–4:30. The main talk starts at 4:40.

Join Zoom Meeting:
Meeting ID: 915 4733 5974