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Explore advanced mathematical structures in topological quantum field theory through this seminar lecture that examines ribbon 2-functors and their applications to higher-dimensional topology. Delve into the categorification of 3D topological quantum field theories and understand how they extend to higher dimensions, focusing on the central concept of ribbon tensor 2-categories. Learn about an innovative approach inspired by derived higher-gauge theory in 4-dimensions that systematically analyzes structures within 2-categories of 2-representations of cobraided dagger Hopf categories. Discover how the interaction between braiding and various levels of duality reveals algebraic and geometric properties of 2-ribbon structures essential for describing framed invariants of knots and surfaces in 4-dimensional space. Gain insights into cutting-edge research addressing the unknowns that currently challenge the field of higher-dimensional topological quantum field theories, with particular emphasis on the mathematical frameworks needed to construct meaningful topological invariants in dimensions beyond three.
