Date: Friday, October 19, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Real Schubert problems, stable curves and tableaux combinatorics
Abstract: Given a finite list of points z_i on the projective line, we can write down a family of enumerative algebraic geometry problems; the simplest of which is to find rational functions with the z_i as critical points. The ShapiroShapiro conjecture, proved by Mukhin, Tarasov and Varchenko, states that, if the z_i are all real, then the solutions to the algebraic geometry problems are all real. I will describe how to extend this result to when the points collide. This will give us a collection of coverings of the moduli space of stable curves. Describing the topology of these coverings recovers standard manipulations of Young tableaux, and provides new explanations for them.
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Speaker: David Speyer
Institution: U. Michigan
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