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RIKEN Center for Advanced Intelligence Project Mathematical Analysis Team

Team Leader: Shin-ichi Ohta (Ph.D.)

Research Summary

Shin-ichi  Ohta(Ph.D.)

My research field is geometry, especially the influence of the curvature to various properties of the space. This area has strong connections with analysis and probability theory. Active interdisciplinary researches include the relation between curvature and the behavior of heat propagation, the geometric structures of spaces consisting of probability distributions, etc. Among them, optimal transport theory, gradient flows of convex functions, and information geometry have tight connections with machine learning as well as information theory. Upon mathematical strengths on these areas, we would theoretically contribute to the field of machine learning.

Research Subjects:

  • Riemannian and Finsler geometries
  • Optimal transport theory
  • Gradient flows of convex functions

Main Research Fields

  • Mathematical & Physical Sciences

Related Research Fields

  • Informatics
  • Interdisciplinary Science & Engineering
  • Geometry
  • Basic analysis
  • Foundations of mathematics/Applied mathematics


  • Optimal transport theory
  • Information geometry
  • Convex optimization
  • Topological data analysis
  • Manifold learning

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.

  • 1. Lebedeva, N., Ohta, S., and Zolotov, V.:
    "Self-contracted curves in spaces with weak lower curvature bound"
    Int. Math. Res. Not. IMRN (2020).
  • 2. Ohta, S. and Takatsu, A.:
    "Equality in the logarithmic Sobolev inequality"
    Manuscripta Math. 162, 271-282 (2020).
  • 3. Ohta, S.:
    "Self-contracted curves in CAT(0)-spaces and their rectifiability"
    J. Geom. Anal. 30, 936-967 (2020).
  • 4. Takatsu, A.:
    "Convergence of combinatorial Ricci flows on tori to degenerate circle patterns"
    Trans. Amer. Math. Soc. 372, 7597-7617 (2019)
  • 5. *Ohta, S. and Palfia, M.:
    "Gradient flows and a Trotter-Kato formula of semi-convex functions on CAT(1)-spaces"
    Amer. J. Math. 139, 937-965 (2017).
  • 6. *Ohta, S. and Palfia, M.:
    "Discrete-time gradient flows and law of large numbers in Alexandrov spaces"
    Calc. Var. Partial Differential Equations 54, 1591-1610 (2015).
  • 7. *Gigli, N., Kuwada, K., and Ohta, S.:
    "Heat flow on Alexandrov spaces"
    Comm. Pure Appl. Math. 66, 307-331 (2013).
  • 8. *Ohta, S. and Sturm, K.-T.:
    "Heat flow on Finsler manifolds"
    Comm. Pure Appl. Math. 62, 1386-1433 (2009).
  • 9. *Ohta, S.:
    "Gradient flows on Wasserstein spaces over compact Alexandrov spaces"
    Amer. J. Math. 131, 475-516 (2009).
  • 10. *Ohta, S.:
    "On the measure contraction property of metric measure spaces"
    Comment. Math. Helv. 82, 805-828 (2007).

Related Links

Lab Members

Principal investigator

Shin-ichi Ohta
Team Leader

Core members

Masayuki Aino
Special Postdoctoral Researcher
Yuka Kotorii
Postdoctoral Researcher
Taiji Marugame
Postdoctoral Researcher

Contact Information

Department of Mathematics, Osaka University
Toyonaka, Osaka 560-0043, JAPAN
Email: shin-ichi.ohta [at] riken.jp