Research Keywords 【 display / non-display

  • Ricci flow

Research Pursuits 【 display / non-display

  • 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

  • Graduate School of Humanities and Sciences, Research Organization, the Core Section The Natural/Applied Sciences Division, Associate Professor

  • Faculty of Core Research Natural Science Division, Associate Professor

  • Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences

  • Graduate School of Humanities and Sciences, Education Organization, Doctral Program Advanced Sciences

  • Graduate School of Humanities and Sciences, Education Organization, Master's Program Advanced Sciences

display all >>

 

Books 【 display / non-display

  • The Ricci flow and the geometric topology of dimension three

    Kyoritsu Shuppan2017.03, TODA Masahito , Research Book

  • 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, Book

Papers 【 display / non-display

  • 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

  • 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

  • On the existence of H-surfaces into Riemannian manifolds

    Calculus of Variations, 1997, Toda,M, Research paper (scientific journal), Single Author

  • 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

  • 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 article

  • 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 article

  • 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 article

Presentations 【 display / non-display

  • Scaling limits of the Ricci flow and monotone quantities

    TODA Masahito, International, 2008.10, International Workshop on Recent Development in Geometry, Invited, Main Speaker

  • 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

  • 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

  • 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

  • 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

display all >>