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Explore the intricate relationship between knot signatures and complex singularities in this advanced mathematical lecture. Delve into Rudolph's conjecture regarding the linear independence of links of irreducible complex curve singularities in the concordance group. Examine Litherland's partial proof of this conjecture and investigate similar questions within the context of deformations of singularities. Learn about the mathematical foundations underlying these concepts and their applications in algebraic topology and complex geometry. Discover how knot theory intersects with the study of complex singularities, with potential extensions to higher-dimensional objects and related mathematical questions. This presentation forms part of a comprehensive mini-course series delivered during the thematic meeting on "Trisections and related topics" at the Centre International de Rencontres Mathématiques in Marseille, France.
