Ben Williams (UBC)

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A1 Homotopy Theory of Stiefel Varieties
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I will present some results about the A1 homotopy of varieties of matrices of maximal rank, and of maps between them. I will explain how the study of these objects may relate the A1 homotopy groups of spheres.

Martijn Kool (UBC)

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Rank 2 sheaves on toric 3-folds
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Let F(q) be the generating function of Euler characteristics of moduli
spaces of rank 2 stable reflexive sheaves on P^3. The action of the
torus on P^3 can be used to compute the fixed locus of the moduli
space and hence F(q). Let G(q) be the generating function of Euler
characteristics of moduli spaces of rank 2 stable torsion free sheaves
on P^3. G(q) can be expressed in terms of F(q) and Euler
characteristics of Quot schemes of certain reflexive sheaves. The
combinatorics of the Quot schemes leads to a new type of box counting
which can be solved in terms of MacMahon functions. Other 3-folds and
relations to Donaldson-Thomas theory (in progress) will be
discussed. Joint work with A. Gholampour and B. Young.

Aaron Bertram (Utah)

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On the cones of effective divisors on the moduli spaces
of sheaves on a surface
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