Date: Friday, September 27, 2013
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: The Expected Codimension of a Matroid Variety
Abstract: Matroid varieties are the closures in the Grassmannian of sets ofpoints defined by specifying which Pl\"ucker coordinates vanish andwhich don't. In general these varieties are very illbehaved, but in many cases one can estimate their codimension by keeping careful track of the conditions imposed by the vanishing of each Pl\"ucker coordinates on the columns of the matrix representing a point of the Grassmannian. We present a way to make this procedure precise, producing a number for each matroid variety called its expected codimension that can be computed combinatorially solely from the list of Pl\"ucker coordinates that are prescribed to vanish. For a special, wellstudied class of matroid varieties called positroid varieties, the expected codimension coincides with the actual codimension.
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Speaker: Nicolas Ford
Institution: U. Michigan
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