Contact: Nitin Chidambaram (kcnitin@mpim-bonn.mpg.de)

Virasoro constraints are often satisfied by generating functions appearing in enumerative geometry. The most famous example is the Witten-Kontsewich partition function, for which one can explicitly write a family of differential operators L_k forming a representation of the Virasoro algebra and such that they annihilate the partition function. One approach to formally study such constraints (and their generalization W-constraints) can be found in the (higher) quantum Airy structures introduced by Kontsevich and Soibelman. In this talk, I will present a family of higher quantum Airy structures coming from the W-algebra of gl_n at the self-dual level found in the work of Borot, Bouchard, Chidambaram, Creuzig and Noshchenko. We will see some applications in Witten r-spin theory and in the open intersection theory of Pandharipande, Solomon and Tessler.

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