"Symplectic invariants" and tau functions: results, conjectures and open questions.

by Nicolas Orantin (CERN)

Tuesday 7 Oct 2008, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

Following the computation of the so-called topological expansion of any observable of the hermitian 1-matrix model proposed by Eynard, it is possible to build out of any algebraic curve (actually not necessary algebraic) a family of "free energies" and "correlation functions" mimicing the topological expansion of the partition function and the observables of random matrix models. In this talk I will review some of the interesting properties satisfied by these objects such as their symplectic invariance, the holomorphic anomaly equation or Hirota bilinear equations. I will also review some of the numerous (integrable) models where these objects can be found, was it proved or just conjectured: random matrix models, enumerative geometry, counting of partitions, topological string theory, statistic of non-intersecting Brownian motions to name a few. This talk intends to be a short overview of this subject and particularly of the open questions it points out.