Topological recursion and quantization: from Eynard-Orantin to Kontsevich-Soibelman frameworks
Bertrand Eynard
IPhT and CRM
Lundi 19/06/2017, 11h00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers

Topological recursion (TR) was invented as a recursive method to enumerate (with a weight) surfaces of genus g and n boundaries. Such enumerative geometry problems can also often be formulated as integrable systems (Dubrovin Zang, Givental) and eventually amount to a quantization procedure. \par Initially in the EO formulation, the data needed for TR was a spectral curve: a plane complex curve, or its generalizations as local plane complex curves. \par In a recent reformulation, Kontsevich and Soibelman proposed to encode the data into an algebraic structure, that they called ``quantum Airy structure'', well suited for the quantization side of the story, and that could possibly allow generalizations. \par We shall discuss the link between the 2, and provide a concise overview of TR and its applications, from enumerative geometry to integrable systems.

Contact : Vincent PASQUIER

 

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