Higher categorical structures in symplectic geometry

We will explore higher categorical structures in symplectic geometry by taking some not entirely rigorous but everthemore instructive shortcuts to the algebraic implications of the analysis of pseudoholomorphic curves. Please come prepared to engage in collective inquiry on questions such as

• Why do pseudoholomorphic disks generate $A_\infty$ algebras?
• What is $A_\infty$ algebra anyways?
• What 2- or $\infty$-categorical structures arise from interpreting string diagrams as pseudoholomorphic curves?