Title: Topological recursion for matrix models and abstract topological recursion (a course of 3 lectures)

Date: 02/15/2017

Time: 3:00 PM - 3:50 PM

Place: C304 Wells Hall

I will begin with the description of a generating function for numbers of
Grothendieck's dessins d'enfant, or Belyi pairs. This generating function
is given by a random matrix model integral, I describe what is a
topological expansion (AKA genus expansion) of such models. The method
allowing finding corrections in all orders of the genus expansion is
Topological Recursion formulated in its present form by Eynard, Orantin
and the speaker in 2005-2006. This method had already found numerous
applications in mathematics and mathematical physics, so I describe the
general construction underlying the topological recursion and present an
(incomplete) list of its applications. Very recently, this method was
developed into an abstract topological recursion by Kontsevich and
Soibelman. In my last lecture I explain their construction and our
interpretation of it (forthcoming paper by J.Andersen, G.Borot, L.Ch., and
N.Orantin).