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Abstract:
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 and Li, Kleitman and
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. In this talk I will discuss the structure of the
defining equations of certain arrangements embedded in reflection
arrangements.
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