Name

OKAWA, Ryo

Official Title

Assistant Professor(without tenure)

Affiliation

(School of Fundamental Science and Engineering)

On-campus Research System

Special Research Project

インスタントンモジュライの代数幾何学的研究

2017

Research Results Outline: ネクラソフ分配関数が満たす関数等式について, 証明を与えた. ネクラソフ分配関数とは, 枠付き連接層のモジュライ上の積分により定義される. 本年度は ネクラソフ分配関数が満たす関数等式について, 証明を与えた. ネクラソフ分配関数とは, 枠付き連接層のモジュライ上の積分により定義される. 本年度は, おもにA_1型特異点の解消上の枠付きモジュライについて考察した. 以前に, 論文1で行っていた... ネクラソフ分配関数が満たす関数等式について, 証明を与えた. ネクラソフ分配関数とは, 枠付き連接層のモジュライ上の積分により定義される. 本年度は, おもにA_1型特異点の解消上の枠付きモジュライについて考察した. 以前に, 論文1で行っていたA_0型特異点, つまり2次元アフィン平面上の結果を拡張した. 手法としては, 望月拓郎氏による壁越えの理論を用いた. 以上の結果は, 業績欄の論文2にまとめた.   さらに, 二つの方向への拡張を試みた. 一つは, 一般のA_n型特異点に対して類似の関数等式を示す試みである. もう一つの拡張として, K理論を用いた積分で定義したネクラソフ分配関数について, 類似の関数等式の導出を試みた. 

インスタントンモジュライの代数幾何学的研究

2018

Research Results Outline: We study moduli of framed sheaves on the projective plane, in particu We study moduli of framed sheaves on the projective plane, in particular, generating functions ofintegrations over mod... We study moduli of framed sheaves on the projective plane, in particular, generating functions ofintegrations over moduli spaces called Nekrasov function. In this year, we try to extend to two cases,1. other surface, 2. K-theory version. In 1. , we computed integrations of other cohomology classes for the minimal resolution of A1 singularity. Although we have not checked rigourously, this could implies that we can construct Painlvé tau function by Fourier transform of Nekrasov functions. Furthermore, towerd other ADE singularities we study finite type quiver varieties as toy models. As a result, we understand that general wall-crossing phenomena are reduced to more fundamental cases.In our case, we study affine quiver varieties, and the minimal resolution of A1 singularity seems fundamental. Hence it seems possible to extend previous results to other ADE singularities soon.  In 2. , we also studied finite type quiver varieties, and also discussed other methods with physicists. 

Lecture Course

Course TitleSchoolYearTerm
Mathematics A2 Kikan(5)School of Fundamental Science and Engineering2019full year@fall semester
Science and Engineering Laboratory 1A IIISchool of Fundamental Science and Engineering2019spring semester
Science and Engineering Laboratory 1A IIISchool of Creative Science and Engineering2019spring semester
Science and Engineering Laboratory 1A IIISchool of Advanced Science and Engineering2019spring semester
Science and Engineering Laboratory 1B IIISchool of Fundamental Science and Engineering2019fall semester
Science and Engineering Laboratory 1B IIISchool of Creative Science and Engineering2019fall semester
Science and Engineering Laboratory 1B IIISchool of Advanced Science and Engineering2019fall semester