- Operator algebra theory: Working on both C*-algebras and von Neumann algebras, particularly in connection with group theory.
- Functional analytic group theory: Studying various aspects of groups by functional analysis methods.
- Quantum information theory: Hanging about Tsirelson's conjecture ( = Kirchberg's conjecture = Connes's embedding conjecture).
- Amenable actions and exactness for discrete groups.
C. R. Acad. Sci. Paris Ser. I Math., 330 (2000), 691--695.
- Homogeneity of the pure state space of
a separable C*-algebra
(in collaboration with Kishimoto and Sakai).
Canad. Math. Bull., 46 (2003), 365--372.
- Solid von Neumann algebras.
Acta Math., 192 (2004), 111--117.
- Amenable Actions And Applications.
International Congress of Mathematicians, Vol. II, 1563--1580,
Eur. Math. Soc., Zürich, 2006.
- Weak amenability of hyperbolic groups.
Groups Geom. Dyn., 2 (2008), 271--280.
- On a class of II_1 factors with at most one Cartan subalgebra
(in collaboration with Popa).
Ann. of Math. (2), 172 (2010), 713--749.
- Noncommutative real algebraic geometry of Kazhdan's property (T).
J. Inst. Math. Jussieu, 15 (2016), 85--90.
- A functional analysis proof of Gromov's polynomial growth theorem.
Ann. Sci. Éc. Norm. Supér. (4), 51 (2018), 549--556.
- Finite-dimensional representations constructed from random walks (slides.pdf)
- Amenability of discrete groups, AIM, September 2016.
- Operator Algebra Seminar, University of Tokyo, November 2016.
- Non-positive curvature group actions and cohomology, Newton Institute, March 2017.
- Special Week on Operator Algebras, Research Center for Operator Algebras (Shanghai), June 2017.
- Von Neumann algebras and measured group theory, Institut Henri Poincaré, July 2017.
- Seminar "Groups, Actions and von Neumann algebras", Université Paris-Sud, September 2017.
- Ergodic and Geometric Group theory in Sendai (EGGS), Tohoku University, October 2017.
- Annual Meeting on Operator Theory and Operator Algebra Theory, Ritsumeikan University, November 2017.
- Operator Algebras and its Application, IPM (Tehran), February 2018. (4 hours)
- 2018 Spring Probability Workshop, Taipei, June 2018.
- Minicourse on Connes's Embedding Problem and its equivalent (A note on Slofstra's work)
- Aut(F_5) has Kazhdan's property (T) (slides.pdf)
- Kyoto Operator Algebra Seminar, RIMS, November 2017.
- Operator Algebra Seminar, University of Tokyo, December 2017.
- Colloquium, UCLA, January 2018.
- Classification of group von Neumann algebras, AIM, January 2018.
- Approximation Properties in Operator Algebras and Ergodic Theory, IPAM, April 2018.
- Interactions between Operator Space Theory and Quantum Probability with Applications to Quantum Information, MFO, May 2018.
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