Ralph Klaasse (ULB) will speak in the geometry seminar on Tuesday 22 January, at 1.30pm in the Salle de Profs. Ralph’s title title is Poisson structures of divisor-type and symplectic Lie algebroids and his abstract is below.
Poisson structures that are generically nondegenerate, such as log- or elliptic Poisson structures, carry an associated divisor ideal which captures their degeneracy. From this we can construct almost-injective Lie algebroids of derivations which are tailor-made to desingularize them. In this talk we discuss the process of lifting Poisson structures of divisor-type (also called almost-regular, after Androulidakis-Zambon) to their (more) nondegenerate Lie algebroid counterparts, and show how the resulting symplectic Lie algebroids can be studied using tools from symplectic geometry. We give an overview of this lifting philosophy, and discuss results that can be obtained using it, such as several existence and obstruction results.