Tropical and log corals with a view towards symplectic cohomology

We will discuss an algebraic-geometric approach to some open invariants arising naturally on the A-model side of mirror symmetry. We will first overview of the use of logarithmic geometry in the Gross–Siebert program. We then will discuss various illustrations of the use in open invariants, including a description of the symplectic Fukaya category via certain stable logarithmic curves. For this, our main object of study will be the degeneration of elliptic curves, namely the Tate curve. However, the results are expected to generalise to higher dimensional Calabi–Yau manifolds.