Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane

Summary: The research explores a surface defect in four-dimensional gauge theories supporting nested instantons, and introduces an effective theory in a specific background. Mathematically conjectural explicit formulae for the virtual equivariant elliptic genus of a certain bundle over the moduli space are derived, with a connection to elliptic cohomology of character varieties and an elliptic version of modified Macdonald polynomials.