In progress
Topological quantum field theories (TQFTs) from unitary tensor categories:
Factorization homology can be used to construct TQFT's with values in C*-categories. I have been developing techniques to compute such theories in dimension 2 when the coefficient disk-algebra is the unitary Drinfel center of the unitary ind-completion of a unitary tensor category. The categories of unitary representations of Drinfeld doubles of compact quantum groups constitute a major class of examples of interest. A guiding principle in this project is to use actions of unitary tensor categories on C*-algebras to give realizations of the TQFT in operator algebraic terms.
Preprints
On the structure of DHR bimodules of abstract spin chains.
arXiv:2504.06094, joint with David Jaklitsch, Corey Jones and Makoto Yamashita.
Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility.
arXiv:2504.05247, joint with Roberto Hernández Palomares.
Injectivity for algebras and categories with quantum symmetry.
arXiv:2205.06663, joint with Makoto Yamashita.
Papers
Actions of Compact and Discrete Quantum Groups on Operator Systems,
Int.Math.Res.Not.IMRN(2024),no.15, 11190-11220, joint with Joeri de Ro.
C*-algebraic factorization homology and realization of cyclic representations.
Quantum Topol. (2024), published online first. DOI 10.4171/QT/212.
Noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of Drinfeld doubles,
J. Math. Pures Appl. (9) (2022), 313-347; MR4377998, joint with Erik Habbestad and Sergey Neshveyev.
Spectral triples and Dixmier trace representations of Gibbs measures: theory and examples,
2024 Nonlinearity 37 105010, joint with Leandro Cioletti, Artur Oscar Lopes and Manuel Stadlbauer.