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Commuting Differential Operators and Spectral Curves

  • Charles Wang (Harvard University)
E1 05 (Leibniz-Saal)

Abstract

I will give a gentle introduction (with computations!) to some ideas related to the KP equation. We will first see pseudo-differential operators, which are linear operators (on a suitable space of functions) containing both differential and integral parts. Next, we will study the ring of commuting differential operators with a given differential operator P, and finally we will see some basic algebraic data associated with P. While this is only a glimpse into a very rich theory, it sets the stage for very interesting objects such as the Sato Grassmannian, Lax pairs, Jacobians, algebraic curves, etc.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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