Faculty of Science Department of Science Assistant Professor
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Updated on 2024/07/03
Ph.D. in Mathematical Sciences ( 2017.3 The University of Tokyo )
Natural Science / Geometry
Niigata University Faculty of Science Associate Professor
2024.7
Country:Japan
Niigata University Faculty of Science Assistant Professor
2020.3 - 2024.6
Country:Japan
Aoyama Gakuin University College of Science and Engineering Teaching Associate (adjunct)
2019.4 - 2020.2
Country:Japan
Tokyo Metropolitan University Graduate School of Science JSPS Research Fellow (PD)
2018.4 - 2020.2
Country:Japan
National Center for Theoretical Sciences (NCTS) Mathematics Division Postdoctoral Fellow
2017.8 - 2018.3
Country:Taiwan, Province of China
Kyushu University Institute of Mathematics for Industry Postdoctoral Researcher
2017.4 - 2017.7
Country:Japan
The University of Tokyo Graduate School of Mathematical Sciences JSPS Research Fellow (DC1)
2014.4 - 2017.3
Country:Japan
Niigata University Faculty of Science Department of Science Assistant Professor
2020.3
The University of Tokyo Graduate School of Mathematical Sciences Doctoral Course
2014.4 - 2017.3
Country: Japan
The University of Tokyo Graduate School of Mathematical Sciences Master Course
2012.4 - 2014.3
Country: Japan
Kyushu University School of Science Department of Mathematics
2008.4 - 2012.3
Country: Japan
The Mathematical Society of Japan
2020.4
Topological complexity of monotone symplectic manifolds Reviewed International journal
Ryuma Orita
Tokyo Journal of Mathematics 47 ( 2 ) 2024
Rigid fibers of integrable systems on cotangent bundles Reviewed International journal
Morimichi Kawasaki, Ryuma Orita
Journal of the Mathematical Society of Japan 74 ( 3 ) 829 - 847 2022.7
Existence of pseudoheavy fibers of moment maps Reviewed International journal
Morimichi Kawasaki, Ryuma Orita
Communications in Contemporary Mathematics 23 ( 05 ) 2050047 - 2050047 2020.7
On the existence of infinitely many non-contractible periodic orbits of Hamiltonian diffeomorphisms of closed symplectic manifolds Reviewed International journal
Ryuma Orita
Journal of Symplectic Geometry 17 ( 6 ) 1893 - 1927 2020.1
Disjoint superheavy subsets and fragmentation norms Reviewed International journal
Morimichi Kawasaki, Ryuma Orita
Journal of Topology and Analysis 13 ( 02 ) 443 - 468 2019.6
Application of fragmentation norms to transported points by Hamiltonian isotopies
Morimichi Kawasaki, Ryuma Orita
RIMS Kôkyûroku 2098 2018.6
Morse-Bott inequalities for manifolds with boundary Reviewed International journal
Ryuma Orita
Tokyo Journal of Mathematics 41 ( 1 ) 113 - 130 2017.12
Non-contractible periodic orbits in Hamiltonian dynamics on tori Reviewed International journal
Ryuma Orita
Bulletin of the London Mathematical Society 49 ( 4 ) 571 - 580 2017.4
Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories Reviewed International journal
Morimichi Kawasaki, Ryuma Orita
Journal of Modern Dynamics 11 313 - 339 2017.4
Linear Mathematics, Third Edition
Tamaki Tanaka, Hideo Kojima, Akinari Hoshi, Ryuma Orita, Nobuhiro Innami, Hisao Yoshihara( Role: Joint author)
Baifukan 2022.4 ( ISBN:9784563012410 )
Floer-type bipersistence modules and rectangle barcodes
Kanta Koeda, Ryuma Orita, Kanon Yashiro
2023.12
Robot motion planning and symplectic geometry
Grant number:21K13787
2021.4 - 2026.3
System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists
Research category:Grant-in-Aid for Early-Career Scientists
Awarding organization:Japan Society for the Promotion of Science
Authorship:Principal investigator Grant type:Competitive
Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )
Applications of periodic orbits in Hamiltonian dynamics and persistence modules
Grant number:20K22302
2020.9 - 2022.3
System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity start-up
Research category:Grant-in-Aid for Research Activity start-up
Awarding organization:Japan Society for the Promotion of Science
Orita Ryuma
Authorship:Principal investigator Grant type:Competitive
Grant amount:\2860000 ( Direct Cost: \2200000 、 Indirect Cost:\660000 )
In this research I dealt with Ginzburg-Gurel conjecture which states that "every Hamiltonian diffeomorphism of closed symplectic manifolds has infinitely many non-contractible periodic orbits, provided that the diffeomorphism has one orbit". Here a manifold is said to be symplectic if it admits a non-degenerate closed two-form. I investigated the problem by assuming some conditions on the fundamental group of the manifold and the symplectic form. Actually, I proved that the conjecture is true for spherically monotone symplectic manifolds whose fundamental group is assumed to be virtually abelian or an R-group.
During the period, I proved that the equivalence between R-groups and torsion-free group of type N. Accordingly, since torsion-free groups of type N are principal, I could apply the theory of Bredon cohomology for them.
Research on applications of Floer theory and persistence modules
Grant number:18J00335
2018.4 - 2021.3
System name:Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows
Research category:Grant-in-Aid for JSPS Fellows
Awarding organization:Japan Society for the Promotion of Science
Authorship:Principal investigator Grant type:Competitive
Grant amount:\3640000 ( Direct Cost: \2800000 、 Indirect Cost:\840000 )
Morse理論の様々な応用に関する研究
Grant number:14J07057
2014.4 - 2017.3
System name:科学研究費助成事業 特別研究員奨励費
Research category:特別研究員奨励費
Awarding organization:日本学術振興会
折田 龍馬
Authorship:Principal investigator Grant type:Competitive
Grant amount:\2500000 ( Direct Cost: \2500000 )
本研究の最終年度は昨年度に引き続き、閉シンプレクティック多様体上のハミルトン力学系における非可縮な周期軌道の存在、特にGurel予想について研究した。Gurel予想はConley予想の変種であり、「閉シンプレクティック多様体上の任意のハミルトニアンは、非可縮周期軌道を少なくとも1つ持てば、無限に多くの非可縮周期軌道を持つ」ということを主張している。Gurel予想はまずGurel自身によって多様体がsymplectically atoroidalな場合に示され、その後GinzburgとGurelによってtoroidally monotoneな場合にまで拡張されている。昨年度私は、両者に当てはまらない多様体である2n次元トーラスについてGurel予想が正しいことを示した。
そこで本年度は、以上の先行研究の拡張を行った。すなわち、基本群がvirtually abelian群かR群である場合に、symplectically asphericalな多様体についてGurel予想が正しいことを示した。さらに、同様の条件を満たす基本群を持つmonotoneな多様体に対しても成り立つことを示した。ここでR群とは、方程式の根が存在すれば一意であるような群である。以上の性質を満たすシンプレクティック多様体としてはトーラスの他に、小平・サーストン多様体や、それらと複素射影空間の直積などが挙げられる。
証明にはフレアー・ノビコフ理論を用いた。フレアー・ノビコフホモロジーでは、その生成元として周期軌道のノビコフ作用を考慮する必要がある。しかし、基本群が上述のようにアーベル群に「近い」性質を持てば、有理ホモトピー論を援用することで、ハミルトニアンのイテレーションによる生成元の変容を記述することが出来た。
Geometry IIA
Level:Undergraduate (specialized) Country:Japan
Geometry IIB
Level:Undergraduate (specialized) Country:Japan
Geometry IA
Level:Undergraduate (specialized) Country:Japan
Geometry IB
Level:Undergraduate (specialized) Country:Japan
Mathematics Exercise B
Level:Undergraduate (liberal arts) Country:Japan
Mathematics Exercise A
Level:Undergraduate (liberal arts) Country:Japan
Introduction to Study "Science, Technology and Society"
Level:Undergraduate (liberal arts) Country:Japan
General Natural Sciences Ⅰ
Level:Graduate (liberal arts) Country:Japan
Primary Seminar in Science
Level:Undergraduate (liberal arts) Country:Japan
Advanced Differential Topology
Level:Postgraduate Country:Japan
The World of Mathematics
Level:Undergraduate (liberal arts) Country:Japan
Seminar in Mathematics
Level:Undergraduate (specialized) Country:Japan
Differential Topology
Level:Postgraduate Country:Japan
Basic Practice on Mathematics a
Level:Undergraduate (liberal arts) Country:Japan
Basic Practice on Mathematics b
Level:Undergraduate (liberal arts) Country:Japan
自然科学総論I
理学基礎演習
理学スタディ・スキルズ
先端科学技術総論
数学講究
微分位相幾何学
数学の世界
幾何学IA
幾何学IB
微分位相幾何学特論
数学基礎演習b
幾何学IIB
数学基礎演習a
幾何学IIA
理学スタディ・スキルズ