Centers & Labs

RIKEN Center for Advanced Intelligence Project

Mathematical Science Team

Team Leader: Kenichi Bannai (D.Math.Sci)
Kenichi  Bannai(D.Math.Sci)

My main area of research is in Arithmetic Geometry, which is a branch of number theory in the filed of pure Mathematics. My research interest is the development of mathematical tools in order to understand conjectures concerning special values of Hasse-Weil L-functions associated to Algebraic Varieties defined over number fields. I hope to apply these and other mathematical tools to the study of machine learning and artificial intelligence.

Main Research Field

Mathematics

Research Subjects

  • Arithmetic Geometry
  • Machine Learning

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.
  1. *Kenichi Bannai, and Shinichi Kobayashi:
    “Integral structures on p-adic Fourier theory”
    Annales de L'Institut Fourier, Vol. 66 no. 2, 521-550 (2016). DOI: 10.5802/aif.3018.
  2. *Kenichi Bannai, Hidekazu Furusho, and Shinichi Kobayashi:
    “p-adic Eisenstein–Kronecker series for CM elliptic curves and the Kronecker limit formulas”
    Nagoya Math. J. 219, 269-302 (2015). DOI: 10.1215/00277630-2891995.
  3. *Kenichi Bannai, and Guido Kings:
    “p-adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields”
    RIMS Kôkyûroku Bessatsu B25: Algebraic Number Theory and Related Topics 2009, eds. T. Ichikawa, M. Kida, T. Yamazaki, 9-30 June (2011).
  4. *Kenichi Bannai, and Guido Kings:
    “p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure”
    American J. Math. 132 no. 6, 1609-1654 (2010).
  5. *Kenichi Bannai, and Shinichi Kobayashi:
    “Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers”
    Duke Math. J. 153 no. 2, 229-295 (2010). DOI: 10.1215/00127094-2010-024.
  6. *Kenichi Bannai, Shinichi Kobayashi, and Takeshi Tsuji:
    “On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves”
    Annales scientifiques de l'ENS 43, fascicule 2, 185-234 (2010).
  7. *Kenichi Bannai, and Shinichi Kobayashi:
    “Algebraic theta functions and Eisenstein-Kronecker numbers”
    RIMS Kôkyûroku Bessatsu B4: Proceedings of the Symposium on Algebraic Number theory and Related Topics, eds. K. Hashimoto, Y. Nakajima and H. Tsunogai, 63--78 December (2007).
  8. *Kenichi Bannai:
    “On the p-adic realization of elliptic polylogarithms for CM-elliptic curves”
    Duke Math. J. 113, 193-236 (2002). DOI: 10.1215/S0012-7094-02-11321-0.
  9. *Kenichi Bannai:
    “Syntomic cohomology as a p-adic absolute Hodge cohomology”
    Math. Z. 242/3, 443-480 (2002). DOI: 10.1007/s002090100351.
  10. *Kenichi Bannai:
    “Rigid syntomic cohomology and p-adic polylogarithms”
    J. Reine Angew. Math. 529, 205-237 (2000). DOI: 10.1515/crll.2000.097.

Lab Members

Principal Investigator

Kenichi Bannai
Team Leader

Core Members

Masahiro Ikeda
Postdoctoral Researcher
Yuuki Takai
Postdoctoral Researcher
Kei Hagihara
Postdoctoral Researcher
Isao Ishikawa
Postdoctoral Researcher
Shuji Yamamoto
Visiting Scientist
Tetsushi Ito
Visiting Scientist
Kota Hattori
Visiting Scientist
Tomoki Kawahira
Visiting Scientist
Yoshiaki Oda
Visiting Scientist
Makiko Sasada
Visiting Scientist
Seidai Yasuda
Visiting Scientist