多复变与复几何研讨班：Generating series of GUE, LUE, and P^1 correlators

摘  要：GUE (Gaussian Unitary Ensemble) and LUE (Laguerre Unitary Ensemble) are two important matrix models. In the first part of this mini-course, we review the fact that their partition functions are tau-functions for the Toda lattice hierarchy. We then review the matrix resolvent method to the study of Toda tau-functions.

摘  要：In this second part of the mini-course, by applying the matrix-resolvent method to Toda tau-functions, we obtain explicit generating series of k-point GUE and LUE correlators. Similar results will also be presented for the Gromov-Witten invariants of the complex projective line. Finally, we study GUE, LUE, and P^1 correlators from the viewpoint of the KP hierarchy.