# Elliptic characteristic classes, bow varieties, 3d mirror duality

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We study elliptic characteristic classes of natural subvarieties in some ambient spaces, namely in homogeneous spaces and in Nakajima quiver varieties. The elliptic versions of such characteristic classes display an unexpected symmetry: after switching the equivariant and the Kahler parameters, the classes of varieties in one ambient space coincide” with the classes of varieties in another ambient space. This duality gets explained as “3d mirror duality” if we regard our ambient spaces as special cases of Cherkis bow varieties. I will report on a work in progress with Y. Shou, based on earlier related works with G. Felder, A. Smirnov, V. Tarasov, A. Varchenko, A. Weber, Z. Zhou.