Rafaelle Vitolo - Università del Salento
27 de setembro, 13h:30-14h:30

The Hamiltonian formulation of Partial Differential Equations is one of the cornerstones of the theory of Integrable Systems. Being carried out by analogy with finite-dimensional Hamiltonian systems, it has an intrinsic geometric nature. In this talk we will review differential-geometric aspects of the Hamiltonian theory of PDEs as well as new projective-geometric properties of known Integrable Systems that are emerging in recent years.

Eduardo Esteves - IMPA
 27 de setembro, 15h e 04 de outubro, 15h

As curves degenerate, their canonical series go along. Where to? Can we describe the limit canonical divisors? We will see through an example that this is not an easy question, as linear equivalence is not preserved under a degeneration.

Indeed, answers were known only in special cases, mainly curves of compact type and curves with two components. Expanding on work by Kapranov and Bainbridge-Chen-Gendron-Grushevsky-Müller, we will describe explicitly all the limits of canonical divisors to a nodal curve which is general for its topology.

Furthermore, we analyze the dependence of the description on the singularity degrees of the degeneration, leading to a polyhedral fan and the construction of a projective variety parameterizing all the limits. This is joint work with Omid Amini (École Polytechnique) and Eduardo Garcez (UECE).