Log geometric techniques for open invariants in mirror symmetry

Log geometric techniques for open invariants in mirror symmetry

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Hülya Argüz , IAS
Fine Hall 322

This is a joint Algebraic Geometry and Symplectic Geometry seminar.  Please note different room (322) and start time (4:30). 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.