Singularity, or a germ of a holomorphic functions, is one of the most classical object of a geometry. This lecture is planned as a quick tour to a classic results about singularities and its categorifications. I will review an Picard-Lefshcetz theory and a critical thrust done by J. Milnor.  Then we will see such topology is inherently symplectic, so that we can talk about their Fukaya categories. This a joint work with Cheol-hyun Cho and Wonbo Jeong.


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