Nekrasov's formula and refined sheaf counting

Nekrasov's formula and refined sheaf counting

Tue, 15/05/2012
15:45 		Balazs Szendroi (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Nekrasov's formula and refined sheaf counting
I revisit the identification of Nekrasov's K-theoretic partition function, counting instantons on $ R^4 $, and the (refined) Donaldson-Thomas partition function of the associated local Calabi-Yau threefold. The main example will be the case of the resolved conifold, corresponding to the gauge group $ U(1) $. I will show how recent mathematical results about refined DT theory confirm this identification, and speculate on how one could lift the equality of partition functions to a structural result about vector spaces.