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Learn about spectral minimal partitions in this 53-minute mathematical physics lecture from the Institute for Advanced Study. Explore how manifolds decompose into disjoint sets while minimizing spectral energy functionals, with particular focus on bipartite and non-bipartite cases. Discover new findings that demonstrate how locally energy-minimizing partitions achieve global minimum status in bipartite scenarios, while operating within specific topological classes for non-bipartite instances. Examine the modified Laplacian operator and Aharonov-Bohm Hamiltonian with singular magnetic potential, essential tools for understanding these topological partition classes. Investigate the geometric structure of minimum states through energy-decreasing deformation techniques applied to critical but non-minimal partitions. Based on collaborative research with Gregory Berkolaiko, Yaiza Canzani, Peter Kuchment and Jeremy Marzuola, presented by Graham Cox from Memorial University of Newfoundland.
