Description:
The lectures are an introduction to different aspects of singularities of algebraic varieties. We present the proof of the Zariski multiplicity conjecture for equisingular families of germs of isolated hypersurface singularities by Bobadilla and Pelka. After reviewing the hybrid geometry behind the A'Campo model of the Milnor fiber and the monodromy, we continue with deriving the McLean spectral sequence converging to the fixed-point Floer homology of the iterates of the monodromy, and apply it to the symplectic version of the monodromy constructed by Bobadilla-Pelka.

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