Oberseminar Deformationsquantisierung und Geometrie: Pablo Nicolás Martínez (Universitat Politècnica de Catalunya, Barcelona)

Abstract:

Cosymplectic structures are natural instances of regular Poisson structures, notably appearing in critical sets of b^m Poisson structures. As the odd-dimensional counterpart of symplectic forms, their study unveils interesting phenomena typically unavailable for broader classes of Poisson structures.

In this talk we present the cosymplectic counterparts of the classical convexity, localization, and surjectivity results in symplectic geometry. For this purpose, we introduce the notion of equivariant cosymplectic structure and show its relation to cosymplectic reduction following Albert. Our proofs are strongly based on the notion of symplectization, yielding a close link between symplectic and cosymplectic structures. This is joint work with Eva Miranda.