Mathematics Colloquia and Seminars

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The mirror symmetry was originally conceived by string theorists in their discovery of two different mathematical formulations of the universe, one using complex holomorphic geometry and the other using symplectic geometry. In algebraic geometry it has been considered as a duality between two families of Calabi-Yau spaces. But the idea of homological mirror symmetry, due to Kontsevich, goes beyond the Calabi-Yau setting. In this introductory talk, I will describe how the generating function of the Catalan numbers appear in this context as a very simple mathematical example of the mirror symmetry. Indeed, this area of research has seen an explosive developments in recent years. This talk is an invitation to this currently extremely hot subject.