Integrability and Applied Algebraic Geometry

Abstracts

Daniele Agostini

Singular curves, degenerate theta functions and KP solutions.

Smooth algebraic curves give rise to solutions to the KP equation via Riemann's theta function. Singular curves produce solutions as well, but the theta function in this case becomes degenerate. I will present some results in this direction, focusing on soliton and rational solutions.

Matt Baker

Analogies between graphs and Riemann surfaces.

I will give a survey of some of analogies and connections between graphs and Riemann surfaces, including graph-theoretic analogues of the Jacobian variety, the Riemann-Roch theorem, and the Riemann-Hurwitz formula. If time permits, I will also discuss the Specialization Lemma and applications to Brill-Noether theory.

Pol Vanhaecke

Toy models for integrability.

In the talk many notions of integrability will be discussed, both in the continuous and discrete cases, and a few conjectures will be formulated. Lotka-Volterra systems will be used as toy models for explaining and comparing these notions.