컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0632 |
|---|---|
| 분류(Section) | Plenary Lecture |
| 분과(Session) | |
| 영문제목 (Title(Eng.)) |
Wild harmonic bundles and some applications |
| 저자(Author(s)) |
Takuro Mochizuki 1 RIMS, Kyoto University1 |
| 초록본문(Abstract) | Harmonic bundles with wild singularities have played important roles in the differential geometric study of holonomic D-modules on algebraic varieties. In this talk, after a brief review of the theory of wild harmonic bundles, we present some applications to related subjects. One is a type of Toda equations. We can classify the real valued solutions of the Toda equations from the viewpoint of the Kobayashi-Hitchin correspondence for wild harmonic bundles. We also have a criterion when the associated semi-infinite variation of Hodge structure has an integral structure. One of the key ingredients is the limit mixed twistor structure with an induced torus action. The other is the Nahm transforms for some types of instantons. Nahm transforms are a differential geometric analogue of Fourier-Mukai transforms. They are procedures to make a type of instantons satisfying some periodicity and boundary conditions from a different type of instantons. Various versions of the Nahm transforms have been studied intensively by many people, but it looks still interesting to clarify the more details on the boundary conditions. We explain our refinement of the Nahm transforms for harmonic bundles and doubly periodic instantons. |
| 분류기호 (MSC number(s)) |
53C07, 34M55, 14H60, 14J60 |
| 키워드(Keyword(s)) | Wild harmonic bundle, Toda lattice, limit mixed twistor structure, instanton, Nahm transform |
| 강연 형태 (Language of Session (Talk)) |
English |