I'll present a new result with A. Mellit, which gives a combinatorial formula for a diagonalizing operator for the modified Macdonald polynomials, known as the nabla operator. This formula was discovered by finding a Schubert-type basis of a certain explicit module from Haiman's polygraph theory, which is conjecturally identified with both the matrix elements of this operator, and the equivariant homology of the unramified affine Springer fiber studied by Goresky, Kottwitz, and Macpherson.

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