06/06/2013, 16:30 — 17:30 — Room P3.10, Mathematics Building
Daniele Sepe, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
Singular integral affine structures and integrable Hamiltonian systems
An important outstanding question in the theory of integrable Hamiltonian systems is their classification, i.e. the construction of some (hopefully computable!) invariants which completely determine these systems up to a suitable notion of equivalence. In this talk, a weaker (but still considerably hard) problem is going to be introduced, namely that of determining when two integrable Hamiltonian systems are equivalent. In the absence of singularities, i.e. equilibria, this problem can be solved using integral affine geometry, which studies symmetries of Euclidean space fixing the standard integral lattice therein; this was first observed by Duistermaat and Dazord and Delzant. One way to extend this result to include singularities is to define an appropriate notion of singular integral affine geometry, which is the aim of this talk. Time permitting, some low dimensional explicit examples will be discussed. This is joint ongoing work with Rui Loja Fernandes.
