Department of Mathematics


  •  Topological recursion for matrix models and abstract topological recursion (a course of 3 lectures)
  •  03/01/2017
  •  3:00 PM - 3:50 PM
  •  C304 Wells Hall
  •  Leonid Chekov, Steklov Institute and MSU

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).



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science