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Explore the algebraic approaches to understanding low-dimensional topological structures in this 52-minute conference talk by A. Beliakova from the University of Zürich. Delve into the mathematical techniques that transform geometric and topological problems into algebraic frameworks, making complex topological concepts more accessible through computational and theoretical methods. Learn how algebraisation serves as a powerful tool for analyzing knots, links, 3-manifolds, and other low-dimensional objects by translating their properties into algebraic invariants and structures. Discover the connections between homological methods, quantum invariants, and computational approaches that have revolutionized the field of low-dimensional topology. Gain insights into current research directions and applications where algebraic methods provide new perspectives on classical topological problems, presented as part of the NCCR SwissMAP workshop on homological, quantum, and computational methods in low-dimensional topology.
