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Paul Johnson : Topology and combinatorics of Hilbert schemes of points on orbifolds

The Hilbert scheme of n points on C^2 is a smooth manifold of dimension 2n. The topology and geometry of Hilbert schemes have important connections to physics, representation theory, and combinatorics. Hilbert schemes of points on C^2/G, for G a finite group, are also smooth, and their topology is encoded in the combinatorics of partitions. When G is a subgroup of SL_2, the topology and combinatorics of the situation are well understood, but much less is known for general G. After outlining the well-understood situation, I will discuss some conjectures in the general case, and a combinatorial proof that their homology stabilizes.

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