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Description

One of active research areas in symplectic 4-manifolds is to cassify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a normal complex surface singularity. Note that the link of a normal complex surface singularity carries a canonical contact structure which is also known as the Milnor Fillable contact structure. One the other hand, algebraic geometers also have studied Milnor fibers as a general fiber of smoothings for a normal complex surface singularity. In this talk, I'd like to explain a relation between minimal symplectic fillings and the Milnor fibers of quotient surface singularities. Furthermore, if a time allows, I'd also like to investigate the relation for weighted homogeneous surface singularities. This is a joint work with Heesang Park, Dongsoo Shin, and Giancarlo Urz\'ua.