July 6: Noah Arbesfeld

Title: Boxcounting and Quot schemes

Abstract:

I'll present concise expressions for the generating series of virtual holomorphic Euler characteristics parametrizing 0-dimensional quotients on C^2 and C^3, along with some generalizations. The formulas in the surface case yield information about certain Nekrasov partition functions, while those for threefolds are related to a conjectural framework of Nekrasov and Okounkov comparing the DT theory of threefolds with the geometry of certain Calabi-Yau fivefolds. Most of what I say will be joint work with Yakov Kononov. I'll also mention some results from work with D. Johnson, W. Lim, D. Oprea and R. Pandharipande.