Amy Wiebe

PDL C-401

The realization space of a polytope is the set of all geometric instances of a particular combinatorial type (face lattice). In this talk we discuss a new model for studying the realization space of a polytope, and we define the ideal on which the model is based, called the *slack ideal *of the polytope.

These ideals were first introduced to study PSD rank of polytopes, and we show how their structure encodes other important polytopal properties, providing a new way to classify projectively unique polytopes and acting as a computational framework for realizability questions. We also show how the model fits related to other more standard realization space models.

**Note: There will be no pre-seminar; only the main seminar talk at 4:10pm.**