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UID:20251110T024456EST-5939rNTkfU@132.216.98.100
DTSTAMP:20251110T074456Z
DESCRIPTION:Seminar Physique Mathématique\n\nTitle: Transalgebraic Spectral
  Curves\, Quantum Curves\, and Atlantes Hurwitz Numbers.\n\nAbstract: Phys
 ics is a great source of ideas for pure mathematics. The topological recur
 sion of Chekhov-Eynard-Orantin (CEO) is an example of this approach: it wa
 s originally developed to solve matrix models in physics\, but was then ab
 stracted away from its physics origins. The result is a mathematical forma
 lism that has found numerous applications in various areas of mathematics\
 , particularly in enumerative geometry. \n	\n	The Topological Recursion/Quan
 tum Curve (TR/QC) correspondence\, which also originated in the context of
  matrix models\, states that the CEO topological recursion (and its higher
  analog)\, which associates a sequence of differentials to a spectral curv
 e\, can be used to reconstruct the WKB asymptotic solution of a differenti
 al equation that is a quantization of the spectral curve (known as a 'quan
 tum curve'). In this work we prove the TR/QC correspondence for a class of
  transalgebraic spectral curves\; those are curves with exponential singul
 arities\, which can be obtained as limits of sequences of algebraic spectr
 al curves. To this end\, we construct a generalization of topological recu
 rsion that is consistent with limits of sequences of algebraic curves\; it
  includes contributions from the exponential singularities. The prototypic
 al example is the spectral curve which is known to give rise to r-spin Hur
 witz numbers via the usual topological recursion\; we show that\, for the 
 same spectral curve\, our natural generalization of the topological recurs
 ion instead computes atlantes Hurwitz numbers\, and reconstructs the WKB s
 olution of the appropriate quantum curve. This is particularly interesting
  given that atlantes Hurwitz numbers had so far evaded topological recursi
 on methods.This is joint work with Reinier Kramer and Quinten Weller.\n\n 
 \n\nZoom : https://umontreal.zoom.us/j/95761000966?pwd=Q3RTdFQ3alVkU3RsWFd
 3UTlxU08z... Meeting ID: 957 6100 0966 / Passcode: 198672\n\n \n\n \n
DTSTART:20220315T193000Z
DTEND:20220315T203000Z
SUMMARY:Vincent Bouchard (University of Alberta)
URL:/mathstat/channels/event/vincent-bouchard-universi
 ty-alberta-338296
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