In this talk, we will review Abouzaid-Smith's proof of formality of the symplectic arc algebra. We will introduce Seidel's formality criterion for A-infinity algebras and Pardon's generalization. In the second part, we will discuss the symplectic geometry of Hilbert schemes of Milnor fibers and explain how this verifies that the formality criterion applies to the symplectic arc algebra. If time permits, we will also indicate some generalizations.
