Department of Mathematics, Aula Magna.
I will discuss a method to associate new algebraic structures with deformations to certain holomorphic Lagrangian fibrations, and describe their relation with other parts of mathematical physics. This algebraic structure controls the enumerative geometry of the variety admitting the Lagrangian fibration in a way analogous to how a quantum group controls the enumerative geometry of a symplectic singularity. Various questions, including the monodromy of the quantum differential equation, can be answered using local-to-global techniques.
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