The topic is ‘Recent advances in Milnor fibrations, deformations and degenerations in algebraic geometry from several modern viewpoints’. Milnor fibration and degeneration of varieties is one of the most classically studied topics in algebraic geometry. It has been addressed from multiple viewpoints: topologically via Picard-Lefschetz theory, via sheaves of vanishing cycles in various categories. New major developments in geometry have motivated new approaches to the same topic from new perspectives. Non-archimedean geometry and the symplectic and Floer theoretic study of degenerations are prominent ones, with possible applications to mirror symmetry. Another very developed topic is the theory of normal surface singularities; in the recent years beautiful connections with the theory of normal surface singularities with Heegard-Floer homology for 3-manifolds have been found and are being developed by A. Nemethi and his school.
The purpose is to treat the same object from different viewpoints in order to foster possible connections. We will focus on non-archimedean and motivic Milnor fibres, symplectic topology and Floer homology of the Milnor fibration, Heegard-Floer and Lattice homologies for surface singularities, and applications of logarithmic geometry to the study of Milnor fibrations.
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