Hiroshi IRIEAssociate Professor
■Researcher basic information
Organization
- College of Science Department of Sciences Mathematics and Informatics
- Graduate School of Science and Engineering（Master's Program） Major in Science
- Graduate School of Science and Engineerin（Doctoral Program） Major in Complex Systems Science
- Faculty of Basic Natural Science Domain of Mathematics and Informatic
Research Areas
■Research activity information
Paper
- Minimal Volume Product of Convex Bodies with Certain Discrete Symmetries and its Applications
Hiroshi Iriyeh; Masataka Shibata, Abstract
We give the sharp lower bound of the volume product of $n$-dimensional convex bodies that are invariant under the discrete subgroups $SO(K)=\{ g \in SO(n); g(K)=K \}$, where $K$ is an $n$-cube or $n$-simplex. This provides new partial results of Mahler’s conjecture and its nonsymmetric version. In addition, we give partial answers for Viterbo’s isoperimetric-type conjecture in symplectic geometry from the view point of Mahler’s conjecture., Oxford University Press (OUP)
International Mathematics Research Notices, 12 Oct. 2022 - Minimal volume product of three dimensional convex bodies with various discrete symmetries
Corresponding
Discrete and Computational Geometry, Oct. 2022, [Reviewed] - Symmetric Mahler's conjecture for the volume product in the three dimensional case
Hiroshi Iriyeh; Masataka Shibata, Corresponding, Duke University Press
Duke Mathematical Journal, 15 Apr. 2020, [Reviewed] - On the structure of the intersection of real flag manifolds in a complex flag manifold
Hiroshi Iriyeh; Takashi Sakai; Hiroyuki Tasaki, 日本数学会
Adv. Stud. Pure Math., Nov. 2019, [Reviewed] - Symplectic topology of Lagrangian submanifolds of CPn with intermediate minimal Maslov numbers
Hiroshi Iriyeh
ADVANCES IN GEOMETRY, Mar. 2017, [Reviewed] - Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces
Hiroshi Iriyeh; Hui Ma; Reiko Miyaoka; Yoshihiro Ohnita
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Oct. 2016, [Reviewed] - Almost all Lagrangian torus orbits in are not Hamiltonian volume minimizing
Hiroshi Iriyeh; Hajime Ono
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, Jul. 2016, [Reviewed] - 複素旗多様体内の実旗多様体の交叉の構造 (部分多様体の微分幾何学の深化)
Iriyeh,Hiroshi; Sakai,Takashi; Tasaki,Hiroyuki, Kyoto University
RIMS Kokyuroku, Apr. 2014 - Lagrangian intersection theory and Hamiltonian volume minimizing problem
Hiroshi Iriyeh; Takashi Sakai; Hiroyuki Tasaki, Springer New York LLC
Springer Proceedings in Mathematics and Statistics, 2014, [Reviewed] - Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type
Hiroshi Iriyeh; Takashi Sakai; Hiroyuki Tasaki, The Mathematical Society of Japan
Journal of the Mathematical Society of Japan, 2013, [Reviewed] - コンパクト型 Hermite 対称空間の実形の対の Floer ホモロジー (部分多様体の微分幾何学的研究)
Iriyeh,Hiroshi; Sakai,Takashi; Tasaki,Hiroyuki, Kyoto University
RIMS Kokyuroku, Jan. 2012 - Tight Lagrangian surfaces in S-2 x S-2
Hiroshi Iriyeh; Takashi Sakai
GEOMETRIAE DEDICATA, Apr. 2010, [Reviewed] - Geodesics of Hofer's metric on the space of Lagrangian submanifolds
Hiroshi Iriyeh; Takashi Otofuji
MANUSCRIPTA MATHEMATICA, Apr. 2007, [Reviewed] - Hamiltonian minimal lagrangian cones in cm
Hiroshi Iriyeh
Tokyo Journal of Mathematics, 2005, [Reviewed] - Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S-2 x S-2
H Iriyeh; H Ono; T Sakai
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, Dec. 2003, [Reviewed] - Infinitesimally holomorphic curves in hyperkähler four-manifolds
Iriyeh; Hiroshi
J. Geom. Phys., 2003, [Reviewed] - Minimal submanifolds in Riemannian spin manifolds with parallel spinor fields
H Iriyeh
JOURNAL OF GEOMETRY AND PHYSICS, Mar. 2002, [Reviewed]
MISC
- Hamiltonian volume minimizing properties of Lagrangian submanifolds (New methods and subjects in submanifold theory and related areas)
Iriyeh Hiroshi; Ono Hajime; Sakai Takashi
RIMS Kokyuroku, Nov. 2004
Lectures, oral presentations, etc.
- On volume product of symmetric convex bodies
Hiroshi Iriyeh
Energies of Knots, Residues of Manifolds and Related Topics, 19 Mar. 2023, Shigehiro Sakata (Fukuoka University), [Invited]
20230318, 20230320 - 凸体のMahler予想について
入江 博
第18回代数・解析・幾何学セミナー, 21 Feb. 2023, 竹内潔(東北大学)、與倉昭治(鹿児島大学)、松村慎一(東北大学)、村上雅亮(鹿児島大学), [Invited]
20230219, 20230221 - 3次元対称凸体のMahler予想の解決
入江 博、柴田将敬
2022年度日本数学会秋季総合分科会, 14 Sep. 2022, 日本数学会, [Invited]
20220913, 20220916 - On Mahler's conjecture for convex bodies
入江 博
大阪市立大学理学部数学教室・数学研究所談話会, 27 Oct. 2021, 大阪市立大学理学部数学教室・数学研究所, [Invited] - On Mahler's conjecture of convex bodies
Hiroshi Iriyeh
第67回幾何学シンポジウム, 02 Sep. 2020, 日本数学会幾何学分科会 勝田篤教授(九州大学)ほか, [Invited]
20200901, 20200903 - A proof of Mahler's conjecture for the volume product of three dimensional convex bodies
Hiroshi Iriyeh
East Asia Symplectic Conference 2019 (台湾, Penghu),, 26 Sep. 2019, Manabu Akaho (Tokyo Metropolitan University), et. al., [Invited]
20190926, 20191002 - On the volume product of three dimensional convex bodies with symmetries of a subgroup of O(3)
Hiroshi Iriyeh
DGA2019--Differential Geometry and its Applications, 03 Sep. 2019, Session organizer: Monika Ludwig (TU Wien; Austria)
20190902, 20190906 - The volume product of convex bodies with discrete symmetries
Hiroshi Iriyeh
Variational problems in Geometry and Mathematical Physics, UK-Japan Winter School, 08 Jan. 2019, Martin Guest (Waseda University), Gerasim Kokarev (University of Leeds),,Reiko Miyaoka (Tohoku University), John C. Wood (University of Leeds), [Invited] - Mahler's conjecture for 3-dim convex bodies and the rigidity of certain symplectic embeddings
Hiroshi Iriyeh
HAYAMA Symposium on Complex Analysis in Several Variables XX＆,Pacific Rim Complex-Symplectic Geometry Conference, 13 Jul. 2018, Xiuxiong Chen (SUNY-Stony Brook), Kengo Hirachi (University of Tokyo), Jun-Muk Hwang (KIAS), Yong-Geun Oh (IBS-CGP), Kaoru Ono (RIMS, Kyoto University), [Invited] - 凸体に関するMahler予想について
入江 博
2017年度福岡大学微分幾何研究集会, 03 Nov. 2017, 佐野友二 教授(福岡大学), [Invited] - 複素射影空間のLagrange部分多様体のホモロジー的剛性について
入江 博
研究集会「対称空間論とその周辺」, 09 Sep. 2017, 井川治 教授(京都工芸繊維大学), [Invited] - On Mahler's conjecture in the three dimensional case
Hiroshi Iriyeh
Singularities Symmetries ＆ Submanifolds, the 18th UK-Japan Winter School in Mathematics, 04 Jan. 2017, [Invited]
20170104, 20170107 - 等径超曲面のGauss像のHamiltonian non-displaceabilityについて
入江博; Hui Ma(中国; 宮岡礼子; 大仁田義裕
日本数学会2016年度年会, 16 Mar. 2016, 日本数学会 - Almost all Lagrangian torus orbits in the complex projective space are not Hamiltonian volume minimizing
Hiroshi Iriyeh
Joint NCTS Differential Geometry and NCKU-RCTS symplectic geometry seminar, 25 Sep. 2015, National Center for Theoretical Sciences Mathematics Division, [Invited]
