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Explore the categorification of Hilbert spaces through this advanced mathematics seminar lecture delivered at the BIMSA-Tsinghua Quantum Symmetry Seminar. Delve into the finite-dimensional notion of 3-Hilbert spaces that categorifies Baez's 2-Hilbert spaces and complex Hilbert spaces, examining how operator algebras over lower Hilbert spaces can be condensed to produce the next categorified level of theory. Learn about the manifestly unitary construction approach and discover recent developments in this cutting-edge area of mathematical research. Gain insights into the intersection of higher category theory, functional analysis, and their applications in quantum symmetry, topological quantum field theory, and condensed matter physics. The presentation builds upon previous work in the seminar series and provides detailed explanations of theoretical frameworks that bridge abstract mathematical concepts with physical applications. Access accompanying slides and reference materials including arXiv:2410.05120 to deepen your understanding of these advanced mathematical structures and their operator algebraic properties.
