Pure Maths Colloquium: Schubert calculus, enumerative geometry and Gelfand-Zetlin polytopes
29 September 2014 16:00 in CM221
Schubert calculus was developed by H.Schubert at the end of the 19th century for solving problems of enumerative geometry. Here is an example of such a problem: how many lines in the three-dimensional space meet four given lines in general position? The answer can be found by studying the intersections of Schubert cycles on a variety of lines in C^4, i.e., the Grassmann variety G(2,4). I will speak about a new approach to Schubert calculus on a closely related family of varieties, i.e., on full flag varieties in C^n. The key idea of this approach comes from toric geometry: we can study the geometry of a full flag variety by looking at the combinatorial structure of a certain polytope, known as the Gelfand-Zetlin polytope.
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