MATUI, Hiroki

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Title
Professor
Field
Operator Algebras
Research interests
K-theory of C*-algebras, minimal dynamical systems
Current research

My research focuses on the study of dynamical systems formed by homeomorphisms on compact spaces, primarily through the lens of C*-algebras, which provide both analytical and algebraic frameworks. My main research themes include K-theoretic classification of C*-algebras, group actions on C*-algebras, classification of minimal dynamical systems up to orbit equivalence, and analysis of topological full groups. In particular, I explore classification of C*-algebras associated with dynamical systems via K-theory, as well as various invariants of groupoids and topological full groups arising from minimal dynamical systems, from a unique perspective where analysis, algebra, and topology intersect. My ongoing research goal is to discover simple and essential structures hidden within the complexity of C*-algebras and dynamical systems.
Selected publications
  1. (With M. Izumi) Poly-Z group actions on Kirchberg algebras II,
    Invent. Math. 224 (2021), 699--766.
  2. (With K. Matsumoto) Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras,
    Kyoto J. Math. 54 (2014), 863--877.
  3. (With Y. Sato) Decomposition rank of UHF-absorbing C*-algebras,
    Duke Math. J. 163 (2014), 2687--2708.
  4. Topological full groups of one-sided shifts of finite type,
    J. Reine Angew. Math. 705 (2015), 35--84.
  5. (With Y. Sato) Strict comparison and Z-absorption of nuclear C*-algebras,
    Acta Math. 209 (2012), 179--196.
  6. Z^N-actions on UHF algebras of infinite type,
    J. Reine Angew. Math. 657 (2011), 225--244.
  7. Homology and topological full groups of etale groupoids on totally disconnected spaces,
    Proc. London Math. Soc. 104 (2012), 27--56.
  8. (With T. Giordano, I. F. Putnam and C. F. Skau) Orbit equivalence for Cantor minimal Z^d-systems,
    Invent. Math. 179 (2010), 119--158.
  9. (With T. Giordano, I. F. Putnam and C. F. Skau) Orbit equivalence for Cantor minimal Z^2-systems,
    J. Amer. Math. Soc. 21 (2008), 863--892.
  10. Some remarks on topological full groups of Cantor minimal systems,
    Internat. J. Math. 17 (2006), 231--251.

Memberships, activities and

Awards

The Mathematical Society of Japan

The Analysis Prize, the Mathematical Society of Japan (2011)

Operator Algebra Prize (Japan) (2012)