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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.

Main Research Fields

  • Mathematics

Research Subjects

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

Selected Publications

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

  • 1.*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).
  • 2.*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).
  • 3.*Ohta, S. and Sturm, K.-T.:
    “Bochner-Weitzenbock formula and Li-Yau estimates on Finsler manifolds”,
    Adv. Math. 252, 429-448 (2014).
  • 4.*Gigli, N., Kuwada, K. and Ohta, S.:
    “Heat flow on Alexandrov spaces”,
    Comm. Pure Appl. Math. 66, 307-331 (2013).
  • 5.*Ohta, S. and Sturm, K.-T.:
    “Non-contraction of heat flow on Minkowski spaces”,
    Arch. Ration. Mech. Anal. 204, 917-944 (2012).
  • 6.*Ohta, S. and Sturm, K.-T.:
    “Heat flow on Finsler manifolds”,
    Comm. Pure Appl. Math. 62, 1386-1433 (2009).
  • 7.*Ohta, S.:
    “Finsler interpolation inequalities”,
    Calc. Var. Partial Differential Equations 36, 211-249 (2009).
  • 8.*Ohta, S.:
    “Gradient flows on Wasserstein spaces over compact Alexandrov spaces”,
    Amer. J. Math. 131, 475-516 (2009).
  • 9.*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

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