Researcher Database

（Last updated : 2024-11-05 12:46:36）　

TARAMA DAISUKE

Department / Course College of Science and Engineering Department of Mathematical Sciences

Title / Position Associate Professor

Other Affiliations
1.	Graduate School of Science and Engineering

Academic background
1.	2012/03 Degree Acquisition	│ Kyoto University Doctor of Informatics
2.	～2007/03	Undergraduate School of Engineering Science │ Faculty of Engineering │ Kyoto University │ Graduated
3.	～2009/03	Master Course │ Department of Applied Mathematics and Physics │ Graduate School of Informatics │ Kyoto University │ Completed
4.	～2012/03	Doctorial Course │ Department of Applied Mathematics and Physics │ Graduate School of Informatics │ Kyoto University │ Completed

Business career
1.	2018/04/01	Associate Professor │ Department of Mathematical Sciences │ Ritsumeikan University,
2.	2016/04/01 ～ 2018/03/31	Assistant Professor │ Department of Mathematical Sciences │ Ritsumeikan University,
3.	2013/04/01 ～ 2016/03/31	JSPS Research Fellow (PD) │ Department of Mathematics │ Kyoto University
4.	2012/10/01 ～ 2013/03/31	Chercheur Post-doctorant │ Laboratoire Jacques-Louis Lions │ Université Pierre et Marie CurieChercheur Post-doctorant
5.	2012/04/01 ～ 2012/09/30	Research Fellow │ Graduate School of Informatics │ Kyoto University

Research activities
1.		Mathematical Society of Japan

Subject of research
1.	Dynamical properties of integrable systems
2.	Geometric studies on integrable systems

Research summary
Theory of integrable systems and geometry The research interests of Daisuke Tarama focus on geometric dynamical systems theory of finite-dimensional completely integrable Hamiltonian systems appearing from analytical mechanics and on related geometries, such as symplectic geometry, Poisson geometry, and algebraic and complex analytic geometry. So far, he has mainly studied mathematics related to free rigid body dynamics describing the motion of rigid body under no external force, as well as their mathematical extensions. The free rigid body dynamics is formulated as a Hamiltonian system on the cotangent bundle over the rotation group of dimension three, whose integrability and the stability of the equilibria are well known since long time ago. Further, the free rigid body dynamics has been extended to completely integrable systems on more general Lie groups from 1970’s. 1. Viewpoint of algebraic and complex analytic geometry: The integrability of the free rigid body dynamics is characterized by the Lax equation and the elliptic curves appearing as spectral curve and the integral curve. In the previous studies, he has studied the geometry and the monodromy of the elliptic fibrations obtained by varying the natural parameters for the free rigid body dynamics in relation to the bifurcation phenomena and the Birkhoff normal forms around the equilibria. He has also studied the relation between the eigenvector mapping for the Lax equation and some Kummer surfaces. 2. Viewpoint of dynamical systems theory: The integrability of the free rigid body dynamics on semi-simple Lie groups has been studied well since 1970’s. However, the stability of its equilibria has been analysed only from 2000’s. He is analysing such stability properties using the techniques in Lie algebra theory and Poisson geometry. Besides, Daisuke Tarama deals with the spectral problem of the differential operators for the quantum systems corresponding to the generalized free rigid body dynamics using the representation theory. He also treats the construction of integrable systems or, more generally, Lagrangian fibrations based on the techniques of complex analytic geometry, such as the theory of elliptic surfaces. He will push forward to researches on the interplay between dynamical systems, including integrable systems, and geometry.

Present specialized field
Geometry, Basic analysis (Keyword：Theory of Integrable Systems, Geometric Mechanics, Dynamical Systems Theory, Algebraic and Complex Analytic Geometry)

Papers
1.	2023/10/28	Rank 5 Trivializable Subriemannian Structure on S^7 and Subelliptic Heat Kernel │ Potential Anal. │ 61,pp.289-316 (Co-authored)
2.	2023/08/01	Geodesic Flows of α-connections for Statistical Transformation Models on a Compact Lie Group │ Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science │ 14072 (2),pp.454-462 (Co-authored)
3.	2022/12/07	Dynamical Systems over Lie Groups Associated with Statistical Transformation Models │ Physical Sciences Forum │ 5 (1),pp.21 (Co-authored)
4.	2021/07/14	Information Geometry and Hamiltonian Systems on Lie Groups. │ Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science, vol 12829. │ (Co-authored)
5.	2020/10/06	Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type │ Research in the Mathematical Sciences │ 7 (32) (Co-authored)
Display All（17）

Competitive grants, etc. (exc. KAKENHI)
1.	2018/11/15 ～ 2019/11/30	Singularity of Dynamical Systems and Geometric Structures │ Research by External Competitive Fund │ Grant for Basic Science Research Projects
2.	2012/10 ～ 2013/03	Geometric and Analytic Study on Integrable Systems │ Research by External Competitive Fund │ Research in Paris 2012

Subject
1.	特殊講義

Message
1.	Research area enriched by geometry and physics The free rigid body dynamics, a typical example of solvable systems in analytical mechanics, is related with many areas in mathematics. To formulate the free rigid body dynamics, techniques in differential geometry are used, such as the theory of Lie group and Lie algebra, symplectic geometry, and Poisson geometry. Since the integral curve and the spectral curve of the Lax equation are elliptic curves, there is also a relation to algebraic and complex analytic geometry. Moreover, the corresponding quantum mechanics requires the methods in representation theory, PDE theory, and functional analysis. The researches on integrable systems connect many different areas of mathematics, particularly of geometry, in a systematic way. I hope to contribute to understanding better this fascinating story woven by geometry and physics.