# Nordita-Uppsala joint seminar on Theoretical Physics

• Datum: –14.15
• Plats: Nordita, Stockholm
• Föreläsare: Rebecca Lodin (1) and Bertrand Eynard (2)
The Tau-function (example KdV) is usually defined as a function of an infinite set of times $t=(t_0,t_1,t_2,t_3,...)$.
Here instead we shall define Tau as a function on the moduli space of spectral curves (plane analytic curves with extra structure), and the "times" can be viewed as local coordinates (but not global in general). The tangent space (i.e. the span of all $\partial/\partial t_k$, i.e. Hamiltonians) to the moduli space of spectral curves, is isomorphic to the space of meromorphic 1-forms on the curve, and by form-cycle duality is isomorphic to a Lagrangian in the space of cycles. In other words, we reinterpret Hamiltonians as cycles, and the symplectic Poisson structure as the intersection of cycles.