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                * Princeton Discrete Math Seminar *
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Date: Thursday 19th November, 3:00 in Fine Hall 224.
 
Speaker: Federico Ardila (San Francisco State)

Title: Positroids, non-crossing partitions, 1/e^2, and a conjecture of
Da Silva

We investigate the role that non-crossing partitions play in the study of
positroids, a class of matroids introduced by Postnikov. We prove that every
positroid can be constructed uniquely by choosing a non-crossing partition on
the ground set, and then freely placing the structure of a connected positroid
on each of the blocks of the partition. We use this to prove that the
probability that a positroid on [n] is connected equals 1/e^2 asymptotically. We
also prove da Silva’s 1987 conjecture that any positively oriented matroid is a
positroid; that is, it can be realized by a set of vectors in a real vector
space. It follows from this result that the positive matroid Grassmannian (or
positive MacPhersonian) is homeomorphic to a closed ball.

This is joint work with Felipe Rincón (Warwick) and Lauren Williams (Berkeley).

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Next week: Thanksgiving. Week after: Peter Winkler

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