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GTC Postdoc Seminar: Positroids, posets and polytopes September 29, 2017 (12:45 PM PDT - 01:30 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Anastasia Chavez (Saint Mary's College of California)
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*** This is a talk to be given at the Modern Math Workshop, a mini-workshop/conference for a general mathematics audience of undergraduates to young faculty. It will also include a small portion about my experience as a MSRI postdoc in the GTC program. The talk will aim to be 30 min. ***

The introduction and study of positroids, a special class of matroids, was pioneered by Postnikov in his study of the totally nonnegative Grassmannian and has subsequently been applied to various fields such as cluster algebras, physics, and free probability. Postnikov showed that positroids, the matroids realized by full rank $k\times n$ real matrices whose maximal minors are nonnegative, are in bijection with several combinatorial objects: Grassmann necklaces, decorated permutations, Le-diagrams and plabic graphs.

This talk will provide an introduction to the theory of positroids. I will also briefly discuss results utilizing this theory that address questions regarding simplicial polytopes and a family of posets called Unit Interval Orders. These results are the product of collaborations with Felix Gotti and Nicole Yamzon.

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