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DTSTAMP;TZID=America/Vancouver:20221208T104500
DTSTART;TZID=America/Vancouver:20221208T104500
DTEND;TZID=America/Vancouver:20221208T112500
UID:20221208T104500@prima2022.primamath.org
SUMMARY:Atlantes Hurwitz numbers and transalgebraic topological recursion
DESCRIPTION:Hurwitz numbers count covers of Riemann surfaces with given ramification data. The case of covers of $\mathbb{P}^1$ with one variable ramifications and a uniform ramification elsewhere is particularly interesting, as these numbers are related to the KP integrable hierarchy. A large family of such Hurwitz problems can be computed using topological recursion: a universal procedure, recursive on the Euler characteristic of the surfaces involved, which requires a spectral curve as input.
The case of Atlantes Hurwitz numbers evaded this approach up to now, as it seemed to have the same spectral curve as completed cycles Hurwitz numbers.
I will introduce all these notions, and explain how Atlantes Hurwitz numbers do satisfy a variant of topological recursion, with a transalgebraic spectral curve, and this distinguishes it from the completed cycles case.
This is joint work with Vincent Bouchard and Quinten Weller.
STATUS:CONFIRMED
LOCATION:Orca
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