Ben Williams (UBC)
A1 Homotopy Theory of Stiefel Varieties
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)
Rank 2 sheaves on toric 3-folds
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)
On the cones of effective divisors on the moduli spaces of sheaves on a surface