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Lax equations and algebraic curves

Luis Felipe Lopez Reyes
Tuesday, October 1, 2019 - 14:00 to 15:00

Many differential equations arising in Mathematics and Physics can be written down in the form of Lax equations. Given a finite dimensional Lax equation depending polynomially on a parameter, we can construct the so called isospectral curve. We will see how the Lax equation induces a flow on the Jacobian of this curve. Using this flow one can write the solutions of the Lax equation in terms of theta functions, we will do this explicitly for the system of equations of a rigid body rotating around a fixed point. Towards the end we will outline how this methods can be extended to the infinite dimensional case. Everybody interested is welcome to attend.

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