APIOS Talk 25 March 2021


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


Read the talk.

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