Field Operator Algebras
Research interests
2-dimensional conformal field theory, topological phases of matter
Current research
I study 2-dimensional conformal field theory from the operator algebraic viewpoint. Rather than using Wightman fields, we deal with a net of operator algebras generated by local observables. The representation theoretic aspects based on the Jones theory of subfactors are mainly focused, and I have close connections to theories of vertex operator algebras and quantum invariants in 3-dimensional topology. Through connections to tensor categories, I also study topological phases of matter.
Selected publications
  1. (with C. E. Sutherland, M. Takesaki) The structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions, Acta Math. 169 (1992), 105-130.
  2. On flatness of Ocneanu's connections on the Dynkin diagrams and classification of subfactors, J. Funct. Anal. 127 (1995), 63-107.
  3. Centrally trivial automorphisms and an analogue of Connes's chi(M) for subfactors, Duke Math. J. 71 (1993), 93-118.
  4. (with J. Bockenhauer, D. E. Evans) On alpha-induction, chiral generators and modular invariants for subfactors, Commun. Math. Phys. 208 (1999), 429-487.
  5. (with R. Longo, M. Mueger) Multi-interval subfactors and modularity of representations in conformal field theory, Commun. Math. Phys. 219 (2001), 631-669.
  6. (with R. Longo) Classification of local conformal nets: Case c < 1, Ann. of Math. 160 (2004), 493-522.
  7. (with R. Longo) Classification of two-dimensional local conformal nets with c < 1 and 2-cohomology vanishing for tensor categories, Commun. Math. Phys. 244 (2004), 63-97.
  8. (with R. Longo) Local conformal nets arising from framed vertex operator algebras, Adv. Math. 206 (2006), 729-751.
  9. (with S. Carpi, R. Longo, M. Weiner) From vertex operator algebras to conformal nets and back, Mem. Amer. Math. Soc. 254 (2018), no. 1213, vi+85 pp.
  10. Conformal field theory, vertex operator algebras and operator algebras, Proceedings of the International Congress of Mathematicians, Vol. III, 2597-2616, World Scientific, Rio de Janeiro, 2018.
(with D. E. Evans) "Quantum Symmetries on Operator Algebras" Oxford University Press (1998).

The Mathematical Society of Japan, American Mathematical Society, International Association of Mathematical Physics

Operator Algebra Prize (2000), The Spring Prize of the Mathematical Society of Japan (2002).
Editors of the following journals: Commun. Math. Phys., Intenat. J. Math., Japan. J. Math., J. Math. Phys. , J. Math. Sci. Univ. Tokyo, Rev. Math. Phys.