Asymptotics + Functional Equations = Exact Quantisation Conditions ?

Duration: 44 mins 57 secs

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Description:	Davide Masoero Universidade de Lisboa 14 June 2021 – 11:10 to 12:10


Created:	2021-06-16 09:36
Collection:	Applicable resurgent asymptotics: towards a universal theory
Publisher:	Isaac Newton Institute for Mathematical Sciences
Copyright:	Davide Masoero
Language:	eng (English)


Abstract:	Since the works of Sibuya, Voros, Dorey-Dunning-Tateo, Bazhanov-Lukyanov-Zamolodchikov, Gaiotto-Moore-Neitzke, Feigin-Frenkel, Masoero-Raimondo-Valeri, Bridgeland, Grassi-Mari˜no, etc...* many exact quantisation schemes have been found employing functional equations, such as the Ysystem or QQ system, that describe the jumps of the asymptotics of Stokes multipliers (or related objects). However, few are the results that actually show that the given functional equations – or the associated nonlinear integral equations, such as the T.B.A. or the D.D.V. equations - admit the expected number of solutions (e.g. Avila 2004, Hilfiker-Runkel 2020). These works are as sparse and deserving as underestimated. In this talk, after having briefly summarised that part of the state-ofthe-art I am expert of, I will describe some of my recent efforts, in collaboration with Riccardo Conti, to prove the ODE/IM correspondence between states of the Quantum KdV model and the monster potentials, using the D.D.V. equation. The talk is based on the paper ‘Counting Monster Potentials’ JHEP 2021 and ongoing work. * I apologise in advance for all the contributions that I will not mention, for lack of time or simple ignorance.

Abstract:

Since the works of Sibuya, Voros, Dorey-Dunning-Tateo, Bazhanov-Lukyanov-Zamolodchikov, Gaiotto-Moore-Neitzke, Feigin-Frenkel, Masoero-Raimondo-Valeri, Bridgeland, Grassi-Mari˜no, etc...* many exact quantisation schemes have been found employing functional equations, such as the Ysystem or QQ system, that describe the jumps of the asymptotics of Stokes multipliers (or related objects). However, few are the results that actually show that the given functional equations – or the associated nonlinear integral equations, such as the T.B.A. or the D.D.V. equations - admit the expected number of solutions (e.g. Avila 2004, Hilfiker-Runkel 2020). These works are as sparse and deserving as underestimated. In this talk, after having briefly summarised that part of the state-ofthe-art I am expert of, I will describe some of my recent efforts, in collaboration with Riccardo Conti, to prove the ODE/IM correspondence between states of the Quantum KdV model and the monster potentials, using the D.D.V. equation.

The talk is based on the paper ‘Counting Monster Potentials’ JHEP 2021 and ongoing work. * I apologise in advance for all the contributions that I will not mention, for lack of time or simple ignorance.

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