Topology, Riemann surfaces
Research interests
moduli of Riemann surfaces, 2-dimensional topology
Current research

My primary interest is in clarifying the topology of Riemann surfaces through the following three infinite-dimensional Lie algebras, (i) the Goldman-Turaev bialgebra, (ii) the associated graded Lie algebra of the Johnson filtration on the Torelli group, and (iii) formal symplectic geometries introduced by Kontsevich. These algebras are connected by (generalized) Magnus expansions of free group.

Selected publications
  1. On the complex analytic Gel'fand-Fuks cohomology of Riemann surfaces, Ann.Inst.Fourier 43(1993), 655-712.
  2. A generalization of the Morita-Mumford classes of extended mapping class groups for surfaces, Invent. math. 131 (1998), 137--149.
  3. (with S. Morita) The primary approximation to the cohomology of the moduli space of curves and cocycles for the stable cohomology classes, Math. Research Lett. 3 (1996), 629-641
  4. (with A. J. Bene and R. C. Penner) Canonical lifts of the Johnson homomorphisms to the Torelli groupoid, Adv. Math., 221(2009) 627--659.
  5. (with Y. Kuno) The logarithms of Dehn twists, Quantum Topology, 5 (2014) 347--423.
  6. (with Y. Kuno) Intersections of curves on surfaces and their applications to mapping class groups, to appear in: Ann. Inst. Fourier 65 (2015) 2711--2762.
  7. (with A. Alekseev, Y. Kuno and F. Naef) Higher genus Kashiwara-Vergne problems and the Goldman-Turaev Lie bialgebra, C. R. Acad. Sci. Paris, Ser. I. vol.355 123--127 (2017)

Memberships, Awards and


Mathematical Society of Japan

Geometry Prize of the Mathematical Society of Japan (2021)