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TODA Masahito
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Research Pursuits 【 display / non-display 】
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The goal is the analysis of the singularity of the Ricci flow. The difficulty of the analysis is whether
one can exclude the flat cone singularity or not.
Assuming the answer is affirmative, the author
works on the symplectic setting on the cotangent
bundle, where the Perelman's L-geodesic equation generates a Hamiltonian flow. He is especially
interested in the relation ship with the geometry
of the loop space of the Ricci flow and the symplectic setting. For instance, applying
the min-max method to the nontrivial homotopy of
the loop space, one obtains a closed geodesic.
This is closely related to the "injectivity radius"
of the loop space and if the "injectivity radius"
has an appropriate lower bound, one can exclude the
flat cone singularity.
Campus Career 【 display / non-display 】
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Graduate School of Humanities and Sciences, Research Organization, the Core Section The Natural/Applied Sciences Division, Associate Professor, 2012.04 - 2015.03
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Faculty of Core Research Natural Sciences Division, Associate Professor, 2015.04 -
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Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences, 2012.04 - 2015.03
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Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences, 2015.04 -
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Graduate School of Humanities and Sciences, Education Organization, Master's Program Advanced Sciences, 2012.04 - 2015.03
Class management data 【 display / non-display 】
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2024
Books 【 display / non-display 】
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幾何学的な線形代数-基礎概念から幾何構造まで
サイエンス社2021.06, 戸田 正人, Textbook, survey, introduction
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３次元リッチフローと幾何学的トポロジー
共立出版2017.03, 戸田 正人, Scholarly book
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３次元トポロジーの新展開 －リッチフローとポアンカレ予想
サイエンス社2007.08, 戸田 正人, Report
Papers 【 display / non-display 】
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Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold
Central European Journal of Mathematics, , 2004, Toda,M, Research paper (scientific journal), Single Author
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On minimizing problem with a volume constraint in hyperbolic 3-manifolds
Annals of global analysis and geometry, , 1999, Toda,M, Research paper (scientific journal), Single Author
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On the existence of H-surfaces into Riemannian manifolds
Calculus of Variations, , 1997, Toda,M, Research paper (scientific journal), Single Author
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Existence and non-existence results of H-surfaces into 3-dimensional Riemannian manifolds
Communications in Analysis and Geometry, , 1996, Toda,M, Research paper (scientific journal), Single Author
Published Article 【 display / non-display 】
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ものの曲がり方とはなんだろうか 〜曲率〜
数理科学, 2014.03, 戸田 正人, Survey, Single Author, Except for reviews, Other
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フィールズ賞業績紹介 ペレルマン
数学セミナー, 2007, 戸田 正人, Survey, Single Author, Except for reviews, Other
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ついに証明されたポアンカレ予想
日経サイエンス, 2004, G.P.コリンズ (訳:戸田正人), Survey, Single Author, Except for reviews, Other
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リッチフロー:極小曲面と三次元多様体
数学セミナー, 2004, 戸田正人, Survey, Single Author, Except for reviews, Other
Presentations 【 display / non-display 】
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リッチフロー上のL幾何
戸田 正人, Domestic, 2009.10, , 最近の解析学の話題おその周辺から, 広島, Invited, Main Speaker
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リッチフローの解析的評価
戸田 正人, Domestic, 2006.11, , 大阪大学幾何セミナー, 大阪大学, 後藤竜二, Invited, Main Speaker
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リッチフローの解析的評価について
戸田正人, Domestic, 2006.11, , 金沢大学数学談話会, 金沢大学, Invited, Main Speaker
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4次元リッチフローの理解に向けて
戸田正人, Domestic, 2006.02, , リーマン幾何と幾何解析, 筑波大学, 山口孝男, Invited, Main Speaker
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リッチ流の基礎
戸田正人, Domestic, 2005.03, , ２１世紀COE物質階層融合科学の構築「春の学校」, 東北大学, 東北大学２１世紀COE物質階層融合科学の構築, Invited, Main Speaker
Receipt of outside funds (Education, Research, Contribution to Society and industry-academia[government] collaboration) 【 display / non-display 】
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Grant-in-Aid for Scientific Research(C)2012, 780,000Thousand yen
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Grant-in-Aid for Scientific Research(C)2011, 650,000Thousand yen
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Grant-in-Aid for Scientific Research(C)2010, 780,000Thousand yen
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Grant-in-Aid for Scientific Research(C)2009, 650,000Thousand yen
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Grant-in-Aid for Scientific Research(C)2008, 780,000Thousand yen