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W$^*$-Bundles and Continuous Families of Subfactors

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OASW01 - Structure of operator algebras: subfactors and fusion categories

W$$-bundles were first introduced by Ozawa, motivated by work on the Toms-Winter Conjecture and, more generally, the classification of C$$-algebras.

I will begin with a brief introduction to W$$-bundles, explaining how they combine the measure theoretic nature of tracial von Neumann algebras with the topological nature of C$$-algebras. I will then discuss the relationship between the triviality problem for W$$-bundles and the Toms-Winter Conjecture. Finally, I will present my work with Ulrich Pennig on locally trivial W$$-bundles and my ongoing work on expected subbundles of W$^*$-bundles inspired by subfactor theory.

This talk is part of the Isaac Newton Institute Seminar Series series.

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