- The poles of the monster potentials asymptotically condensate about the complex equilibria of the ground state potential.
- The leading correction to such asymptotics is described by the roots of Wronskians of Hermite polynomials.

This allows me to associate to each partition of N a unique monster potential with N roots, of which I compute the spectrum. As a consequence, I prove up to a few mathematical technicalities that, fixed an integer N, the number of monster potentials with N roots coincide with the number of integer partitions of N, which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.

This is joint work with Riccardo Conti (Group of Mathematical Physics of Lisbon University).

]]>Conformal nets are one of the existing axiomatizations of chiral conformal field theory (vertex operator algebras being another one). We will show that, given an arbitrary conformal net and a surface with boundary $\Sigma$, we get a continuous projective unitary representation of the relative mapping class group (orientation reversing elements act by anti-unitaries). When the conformal net is rational and $\Sigma$ is a closed surface (i.e. $\partial \Sigma = \emptyset$), then these representations are finite dimensional and well known. When the conformal net is not rational, then we must require $\partial \Sigma \neq \emptyset$ for these representations to be defined. We will try to explain what goes wrong when $\Sigma$ is a closed surface and the conformal net is not rational.

The material presented in this talk is partially based on my paper arXiv:1409.8672 with Arthur Bartels and Chris Douglas.

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