Mirror symmetry, a vast conjectural dictionary relating symplectic geometry to algebraic geometry, has fascinated mathematicians since it was predicted by physicists around 1990.

This lecture series focuses on two key conjectures in the field, Kontsevich's homological mirror symmetry (1994) and the Strominger-Yau-Zaslow (SYZ) conjecture (1996). The first lecture will give an elementary introduction to the subject for non-specialists. We will see in particular how the very simplest instance of homological mirror symmetry relates counts of triangles on a torus to the classical Jacobi theta function.

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