#TodaysMath
I am currently learning the hard way that the #FukayaCategory of even very simple objects (still thinking about these surfaces with singular symplectic structures) can have lots of higher \(A_{\infty}\)-operations that are very easy to overlook! Counting polygons is surprisingly hard when they have weird shapes. 🙃

#TodaysMath is still the #FukayaCategory for log #symplectic surfaces.
Log symplectic structures on oriented closed surfaces are one of the relatively few classes of #Poisson #manifold that are fully classified:
https://arxiv.org/abs/math/0110304
The classification was done by Olga Radko in this paper, where they are called topologically stable Poisson structures (since their degeneracy locus is stable under small perturbation).
The paper is self-contained and readable with few prerequisites, have a look!

So, #TodaysMath is figuring out the higher operation in the #FukayaCategory for a real log #symplectic surface, meaning a surface with a particular "nice" singularity on a collection of embedded circles. These circles divide the surface into multiple symplectic components, but the components are not all separate! They interact with each other in the Fukaya category.