Seminar: Sergei Lando (Higher School of Economics, Moscow)

Title: Combinatorial solutions to integrable hierachies

2015.01.21 | Jane Jamshidi

Date Tue 27 Jan
Time 16:15 17:15
Location 1531-113 (Aud. D1)


Integrable hierarchies of partial differential equations appeared as a tool to describe the
behavior of waves of special kind. It happened, however, that their solutions include very interesting
formal ones, whose coefficients give answers to natural enumerative problems. According
to Sato construction (1980), these solutions can be expressed in terms of Young diagrams and
Schur polynomials. A spectacular example of such solution is the Witten–Kontsevich potential,
which is the generating function for certain geometric parameters of moduli spaces of complex
structures on curves. For such solutions, the equations of the hierarchies can be interpreted
as recurrence relations allowing one to efficiently compute the coefficients of the corresponding
formal power series.

It will be explained how to construct solutions to the Kadomtsev–Petviashvili integrable
hierarchy by means of Schur polynomials, and examples will be given, including those found
recently, of enumerative problems leading to such solutions.