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John Baez (Sep 24 2020 at 22:11):My student @Joe Moeller is working with an undergrad, Sadaf Kadir, on a project involving 2d TQFT. I'm wondering if anyone has looked at the partition function as a function of genus and differentiated it with respect to the genus. This is a strange thing to do since the genus takes integer values... but in the limit of large genus it should make sense and have some physical meaning: derivatives of the partition function tend to be important in statistical mechanics and quantum mechanics.
Probably someone has done this before... and that's okay, because this project doesn't need to be original research. But I'm wondering about the physical interpretation. For example Coleman did calculations involving a 'gas of virtual wormholes', claiming to show this drives the cosmological constant down to zero. There might be a lower-dimensional (and purely topological) analogue of that here.