RIKEN Center for Advanced Intelligence Project Mathematical Analysis Team
Team Leader: 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
- Riemannian and Finsler geometries
- Optimal transport theory
- Gradient flows of convex functions
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).
- Shin-ichi Ohta
- Team Leader
- Yuka Kotorii
- Postdoctoral Researcher
Department of Mathematics, Osaka University
Toyonaka, Osaka 560-0043, JAPAN