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SUMMARY:Séverin Charbonnier (IRIF\, CNRS/Université de Paris)
DTSTART:20220620T090000Z
DTEND:20220620T100000Z
DTSTAMP:20260423T024456Z
UID:IPHT-PHM/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IPHT-PHM/5/"
 >Geometric recursion on combinatorial Teichmüller space</a>\nby Séverin 
 Charbonnier (IRIF\, CNRS/Université de Paris) as part of Séminaire de ph
 ysique mathématique IPhT\n\nLecture held in Salle Claude Itzykson\, Bât.
  774\, Orme des Merisiers.\n\nAbstract\nGeometric recursion is a procedure
  developed in 2017 by J.E. Andersen\, G. Borot and N. Orantin\, which gene
 ralizes topological recursion. For specific choices of the initial data an
 d of the target theory on which the recursion runs\, it allows to recursiv
 ely construct objects that capture geometric properties of surfaces that a
 re useful in mathematical physics. Together with J.E. Andersen\, G. Borot\
 , A. Giacchetto\, D. Lewański and C. Wheeler\, we have established a seri
 es of results allowing to promote the combinatorial Teichmüller space to 
 a target theory for geometric recursion.\n\nI will first describe the comb
 inatorial Teichmüller space and some of its properties\; second I will de
 fine geometric recursion (GR) on this space. I will then give two instance
 s of this recursion: the first one is akin to Mirzakhani–McShane identit
 y\, the second one is a recursive formula for the count of multicurves on 
 combinatorial surfaces. Last\, I will expose a set of coordinates on the c
 ombinatorial Teichmüller space that is well-suited for geometric recursio
 n. Those coordinates allow to recover topological recursion via a procedur
 e of integration: in particular for the 2 instances of the talk\, we get a
 nother proof of Witten's conjecture and a recursive formula for Masur–Ve
 ech volumes.\n
LOCATION:https://researchseminars.org/talk/IPHT-PHM/5/
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