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Slack Realization Space of a Matroid
Algebraic Geometry and Number Theory| Speaker: | Madeline Brandt, UC Berkeley |
| Related Webpage: | https://math.berkeley.edu/~brandtm/ |
| Location: | 2112 MSB |
| Start time: | Wed, Oct 10 2018, 1:10PM |
In this talk I will introduce a new model for the realization space of a matroid which is cut out by equations from a saturated determinantal ideal, called the slack ideal, coming from the vertex-hyperplane incidence matrix of the matroid. This is inspired by a similar model for the slack realization space of a polytope. I will demonstrate how to use these ideas to certify non-realizability of matroids and exhibit a way of detecting projectively unique matroids via their slack ideals by introducing a toric ideal that can be associated to any matroid. In the talk I will emphasize and carry out examples.