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SUMMARY:Resurgence\, Stokes Constants\, and Arithmetic Functions in  Topol
 ogical String Theory
DTSTART:20230413T123000Z
DTEND:20230413T133000Z
DTSTAMP:20260506T124500Z
UID:indico-event-9650@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Claudia Rella (University of Geneva & IHES)\n\nThe q
 uantization of the mirror curve to a toric Calabi-Yau threefold gives rise
  to quantum-mechanical operators. Their fermionic spectral traces produce 
 factorially divergent power series in the Planck constant\, which are conj
 ecturally captured by the refined topological string in the Nekrasov-Shata
 shvili limit via the Topological Strings/Spectral Theory correspondence. I
 n this talk\, I will discuss how the machinery of resurgence can be applie
 d to study the non-perturbative sectors associated with these asymptotic e
 xpansions\, producing infinite towers of periodic singularities in the Bor
 el plane and infinitely-many rational Stokes constants\, which are encoded
  in generating functions given in closed form by q-series. I will then pre
 sent an exact solution to the resurgent structure of the semiclassical lim
 it of the first fermionic spectral trace of the local P2 geometry\, which 
 unveils a remarkable arithmetic construction. The same analytic approach i
 s applied to the dual weakly-coupled limit of the conventional topological
  string on the same background. The Stokes constants are explicit divisor 
 sum functions\, the perturbative coefficients are particular values of kno
 wn L-functions\, and the duality between the two scaling regimes appears i
 n number-theoretic form. This talk is based on arXiv:2212.10606.  Pour 
 être informé des prochains séminaires vous pouvez vous abonner à la li
 ste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec co
 mme sujet: "subscribe seminaire_mathematique PRENOM NOM"(indiquez vos prop
 res prénom et nom) et laissez le corps du message vide. \n\nhttps://indi
 co.math.cnrs.fr/event/9650/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/9650/
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