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Monday, March 13, 2017

**Abstract:** A star log symplectic bi-vector on a surface has a degeneracy loci locally modelled by a finite set of lines in the plane intersecting at a point. We will discuss two ways to capture the behaviour of their deformations: one `global' and one more `local' in flavor. From a global perspective, we classify all star log symplectic structures on compact surfaces up to symplectomorphism by some associated Lie algebroid de Rham cohomology classes. In a more local snap shot, we compute the Poisson cohomology of these structures and discuss the relationship of our classification and the second Poisson cohomology.