Prof. Di Yang
On tau-functions for the KdV hierarchy
For an arbitrary solution to the KdV hierarchy, we give an expression of
the generating series of logarithmic derivatives of the tau-function of the
solution explicitly in terms of the so-called basic matrix resolvent. Based
on this we develop two new formulae for the generating series by
introducing a pair of wave functions of the solution. Applications to the
Witten–Kontsevich tau-function, to the generalized BGW tau-function,
as well as to a modular deformation of the generalized BGW
tau-function will be given.
The talk is based on a series of joint works with Marco Bertola, Boris Dubrovin and Don Zagier.
Thursday 25 March 2021, 10AM Beijing Time