A new perspective on the 2D Toda-RS correspondence
Matej Penciak - Northeastern University
The 2D Toda system consists of a complicated set of infinitely many coupled PDEs in infinitely many variables that is known to assemble into an infinite-dimensional integrable system. Krichever and Zabrodin made the remarkable observation that the poles of some special meromorphic solutions to the 2D Toda system are known to evolve in time according to the Ruijsenaars-Schneider many particle integrable system. In this talk I will describe work in progress to establish this 2D Toda-RS correspondence via a Fourier-Mukai equivalence of derived categories: a category of ``RS spectral sheaves'' on one side, and a category of "Toda micro-difference operators" on another. This description of the 2D Toda-RS correspondence mirrors that of the KP-CM corrspondence previously established by two of the authors and suggests the existence of a conjectural elliptic integrable hierarchy.