: I will discuss a conjectural definition of refined curve counting invariants of
Calabi-Yau threefolds with a C*-action in terms of stable maps on Calabi-Yau
fivefolds. The corresponding disconnected generating function should conjecturally
equate the Nekrasov-Okounkov K-theoretic membrane index under a refined version of the
Gromov-Witten/Pandharipande-Thomas correspondence. I'll present several acid tests
validating the conjecture, both in the A and the B-model. This is based on joint work
with Yannik Schuler (ETH Zurich), arXiv:2410.00118.
https://arxiv.org/abs/2212.00320
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