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
Monadic reconstruction of unitary Drinfeld centers and Factorization Homology
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.
Accepted for publication at Glasgow Mathematical Journal.
Injectivity for algebras and categories with quantum symmetry.
arXiv:2205.06663, joint with Makoto Yamashita.
Categorical dualtiy for Yetter-Drinfeld C*-algebras. Beyond the braided-commutative case
arXiv:2504.21162 , joint with Makoto Yamashita.
Accepted for publication at Annales Mathématiques Blaise Pascal.
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.