Spring 2012 Seminar Series

DATE: April 19th
LOCATION: E51-335
TIME: 4:15pm
Reception immediately following in the ORC Conference Room (E40-106)

SPEAKER:
Santanu Dey

TITLE
Some properties of convex hulls of integer points contained in general convex set

ABSTRACT
In this talk, we present properties of general closed convex sets that determine the closedness and polyhedrality of the convex hull of integer points contained in it. We first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed. This leads to useful results for special classes of convex sets such as pointed cones, strictly convex sets, and sets containing integer points in their interior. We then present sufficient conditions for the convex hull of integer points in general convex sets to be polyhedron. These sufficient conditions generalize the sufficient conditions given in Meyer (1974). Under a simple technical condition, we show that these sufficient conditions are also necessary conditions for the convex hull of integer points contained in general convex sets to be a polyhedron.

 

This is joint work with Diego A. Moran R.