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Colloquium
Seminar information archive ～10/10｜Next seminar｜Future seminars 10/11～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
Next seminar
2024/10/25
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Hokuto Konno (Graduate School of Mathematical Sciences, The University of Tokyo)
Diffeomorphism group and gauge theory (JAPANESE)
https://forms.gle/96tZtBr1GhdHi1tZ9
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Hokuto Konno (Graduate School of Mathematical Sciences, The University of Tokyo)
Diffeomorphism group and gauge theory (JAPANESE)
[ Abstract ]
The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. On the other hand, in the topology of manifolds, the diffeomorphism group, which is the automorphism group of a given smooth manifold, is a fundamental object of interest. Even for higher-dimensional manifolds, whose classification was largely settled more than half a century ago, significant progress continues to be made, and this remains a major trend in recent topology. Nevertheless, the systematic study of the diffeomorphism groups of 4-dimensional manifolds, particularly from the perspective of gauge theory, had long remained underexplored, with only a few pioneering results. However, in recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.
[ Reference URL ]The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. On the other hand, in the topology of manifolds, the diffeomorphism group, which is the automorphism group of a given smooth manifold, is a fundamental object of interest. Even for higher-dimensional manifolds, whose classification was largely settled more than half a century ago, significant progress continues to be made, and this remains a major trend in recent topology. Nevertheless, the systematic study of the diffeomorphism groups of 4-dimensional manifolds, particularly from the perspective of gauge theory, had long remained underexplored, with only a few pioneering results. However, in recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.
https://forms.gle/96tZtBr1GhdHi1tZ9
