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Colloquium
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html |
2009/07/24
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Carlos Simpson (CNRS, University of Nice)
Differential equations and the topology of algebraic varieties
Carlos Simpson (CNRS, University of Nice)
Differential equations and the topology of algebraic varieties
[ Abstract ]
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of ``Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of ``shape'' and nonabelian cohomology.
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of ``Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of ``shape'' and nonabelian cohomology.
