We would like to discuss an algebraic-geometric approach to some open
invariants arising naturally on the A-model side of
mirror symmetry. The talk will start with a smooth 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. This is joint work with Bernd Siebert, with
general ideas based on discussions of Bernd Siebert and Mohammed
Abouzaid.