Speaker
Prof.
Jørgen Vold Rennemo
Description
In recent work, Arbesfeld, Kool, and Lim, following work in physics by Nekrasov, studied the moduli space of representations of a quiver with relations called the 4D ADHM quiver. In particular, they placed Nekrasov’s partition function on a rigorous algebro-geometric footing using the fourfold counting invariants of Oh–Thomas.
In the same paper, they conjectured that the moduli space of stable framed representations of this quiver is isomorphic to a moduli space of two-dimensional framed sheaves on $(\mathbb{P}^1)^4$. This generalizes a result going back to Barth, which identifies representations of the ADHM quiver with torsion-free framed sheaves on $\mathbb{P}^2$.
I will explain these results and present a proof of the conjecture.