Speaker: Thomas VandenBoom, Department of Mathematics, Yale University

Title: Bilateral periodicity of stationary solutions of the Toda flow 

Abstract: Classically, the Toda flow is a spectrum-preserving flow on symmetric tridiagonal Jacobi matrices described by a simple system of ODEs. Asymptotically, this flow tends to a diagonalization of the initial condition, and the stationary points of the flow are precisely diagonal matrices. The same system of ODEs extends naturally to a hierarchy of flows on Jacobi operators acting on the integer lattice, whose stationary solutions are much more interesting: their parametrizing sequences are almost-periodic. In this talk, we will investigate how "almost" periodic these solutions can be; in particular, we will show that, for certain Toda flows, stationary Jacobi operators with periodic off-diagonal must have periodic main diagonal.

(Joint work with Lance Saddler, Tony Zeng, and Richard Zhou.) 

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