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複素解析幾何セミナー
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| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
2011年06月27日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
斎藤恭司 氏 (東京大学 IPMU)
Vanishing cycles for the entire functions of type $A_{1/2\infty}$ and $D_{1/2\infty}$ (JAPANESE)
斎藤恭司 氏 (東京大学 IPMU)
Vanishing cycles for the entire functions of type $A_{1/2\infty}$ and $D_{1/2\infty}$ (JAPANESE)
[ 講演概要 ]
We introduce two elementary transcendental functions $f_{A_{1/2\infty}}$ and $f_{D_{1/2\infty}}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{1/2\infty}$ and $D_{1/2\infty}$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space. All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.
We introduce two elementary transcendental functions $f_{A_{1/2\infty}}$ and $f_{D_{1/2\infty}}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{1/2\infty}$ and $D_{1/2\infty}$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space. All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.
