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    神楽坂微分幾何学セミナー
               今後の予定  

日時 : 4月27日(土) 15:00〜17:15
 場所 : 東京理科大学神楽坂キャンパス331教室
   15:00〜16:00
    講演者 : 小林 穂乃香 (東京理科大学)
    講演タイトル : 擬双曲空間内の平均曲率一定な部分多様体
            の擬双曲的ガウス写像
    アブストラクト :
We investigated oriented surfaces of constant mean and
Gaussian curvatures and non-diagonalizable shape operator in pseudo-hyperbolic space.
It is known that such Lorentzian surfaces in 3-dimensional anti-de Sitter space are
either a B-scroll or a complex circle.In this talk, we first state result for the type numbers
of the pseudo-hyperbolic Gauss maps of a B-scroll and a complex circle.

Secondly, we state results for the type numbers of the pseudo-hyperbolic Gauss maps of
generalized umbilical hypersurfaces which are a natural generalizations of B-scrolls in the
general dimensional anti-de Sitter space.
Also, we state constructions of consider as
surfaces can be generalized umbilical hypersurfaces in the pseudo-hyperbolic space and
pseudo-sphere of index 2 and B-scroll in 5-dimensional pseudo-hyperbolic space of index 2.

This talk is based on a joint work with Naoyuki Koike.


   16:15〜17:15
    講演者 : 本田 淳史 (横浜国立大学)
    講演タイトル : 3次元ローレンツ多様体内の有界なガウス曲率
            を持つ混合型曲面
    アブストラクト :
A mixed type surface is a connected regular surface in
a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced
metric of a mixed type surface is a signature-changing metric, and their lightlike points
may be regarded as singular points of such metrics. In this talk, we investigate the behavior
of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface.
To characterize the boundedness of Gaussian curvature at a non-degenerate lightlike
points, we introduce several fundamental invariants along non-degenerate lightlike points,
such as the lightlike singular curvature and the lightlike normal curvature. Moreover, using
the results by Pelletier and Steller, we obtain the Gauss-Bonnet type formula for mixed
type surfaces with bounded Gaussian curvature. This talk is based on a joint work
(arXiv:1811.11392) with K. Saji (Kobe University) and K. Teramoto (Kyushu University).


          2019年度の記録


  日時 : 3月2日(土) 16:00〜17:00
  場所 : 東京理科大学神楽坂キャンパス341教室(3号館4階)
  講演者 : Alexander Hock (ミュンスター大学)
  講演タイトル : Exact solution of matricial \phi^3_2 model to
           all genus by topological recursion
  講演アブストラクト :
Developed methods will be extended to find exact solution
        for the \phi_2^3 matrix model with an external matrix E in the large N limit.
        This model can be understood as regularized Kontsevich model, where the
        regularization ensures UV finiteness in 2 dimensions in case of linear eigen
        values.
The universal structure of topological recursion is used and slightly
        affected by the regularization for the one boundary (puncture) sector.
        All correlation functions of genus g with B boundary components are achieved
        by a differential operator A_X acting on the one boundary solution. The results
        are exact and describes the summation of all weighted 3 valent graphs on
        a B-punctured Riemann surface of genus g. Even though a \phi^3 model is
        unstable, it arises as a exactly solvable noncommutative qunatum field theory
        on a highly deformed Moyal space.


            
2018年度の記録

  日時 : 12月22日(土) 15:30〜17:45
  場所 : 東京理科大学神楽坂キャンパス233教室
    15:30〜16:30
     講演者 : 國川 慶太 (東北大学)
     講演タイトル : ハイパーケーラー多様体の中の平均曲率流
     講演アブストラクト :

      Leung-Wanはハイパーケーラー多様体の中で, ハイパーラグランジュ部分多様体
        という概念を導入し,この性質が平均曲率流に沿って保たれることを示した.
        本講演では,ハイパーラグランジュ部分多様体に対して自然に定義される
        「ツイスターエネルギー」というものを新たに考え, 十分小さいツイスターエネルギー
        を持つハイパーラグランジュ部分多様体が平均曲率流に沿って複素ラグランジュ
        部分多様体に収束することを紹介する.
        なお,この講演は高橋良輔氏との共同研究に基づく.

       .

    16:45〜17:45
     講演者 : 新田 泰文 (東京理科大学)
     講演タイトル : Uniform relative stability and coercivity
              for polarized toric manifolds
     講演アブストラクト :
      
We study a relation between algebro-geometric stability and the growth of
        the modified K-energy which characterizes the extremal K
ahler metric as
        a critical point. In this talk, we introduce uniform relative K-polystability
        for polarized toric manifolds and show that it implies the coercivity of the
        modified K-energy modulo the maximal torus action. If time allows, we will
        also discuss on the converse direction. 
        This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.


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   世話人: 小池 直之,田中 真紀子,佐古 彰史,新田 泰文,馬場 蔵人,只野 誉,山本 光

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