Mathematics Colloquia and Seminars

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Questions involving arrangements of linear subspaces arise in connection with a wide range of topics in mathematics including invariant theory, graph theory, and algebraic geometry. Surprisingly, if the subspaces have codimension greater than one, the equations defining the arrangement are quite mysterious in general. However, results of Li-Li, Kleitman-Lovasz, De Loera, and Domokos have shown that the defining equations of certain classes of arrangements with a high degree of symmetry have very beautiful descriptions. I'll discuss arrangements consisting of the i-dimensional faces of an n-dimensional cube. In particular, I'll describe their defining equations and show that these equations form a Groebner basis under very mild conditions on the term ordering.