Yunhyung Cho, Monotone Lagrangian Tori in Fano Varieties

This is a survey talk of current progress of mirror symmetry of Fano varieties. For a given smooth Fano variety X, it has been conjectured that there exists a Laurent polynomial called a (weak) Landau-Ginzburg mirror (or weak LG mirror shortly) which encodes a quantum cohomology ring structure of X. Tonkonog proved that one can find a weak LG mirror using a monotone Lagrangian torus in X. In this talk I will explain how to find a monotone Lagrangian torus using a Fano toric degeneration of X. If time permits, I will also describe a monotone Lagrangian torus in a given flag variety.