Soren Gammelgaard

I am interested in moduli spaces attached to the action of finite groups on affine spaces, and their connections with quiver varieties.

For instance, we can let G be a finite subgroup of $ SL_2(\mathbb C)$: then we can consider the symmetric powers of the singularity $X=\mathbb C^2/G$, the punctual Hilbert schemes $\operatorname{Hilb}^n X$, or the same constructions with the minimal resolution of X in its place. Generalising, we can also consider spaces of torsion-free sheaves on these singularities or their resolutions - to make the theory work well, it usually becomes necessary to compactify these singularities, for instance as Deligne-Mumford stacks.

Many of these spaces can be constructed as quiver varieties, which is the focus of my research.

For more details on my current and future research, please see https://sorengam.github.io/research_detailed.

I am also interested in:

• Grothendieck rings of varieties
• Hodge Theory
• Fano schemes and cubic hypersurfaces (this was the subject of my master's thesis).