理化学研究所 数理創造プログラム (iTHEMS) 客員研究員
本務: 東京大学大学院 数理科学研究科 助教
今野 北斗 Hokuto Konno
- 2019-04-01 - 2020-03-31 基礎科学特別研究員
- 2020-05-01 - 客員研究員
I have been working in the mathematical study of gauge theory. In particular, I have developed Seiberg-Witten theory and Yang-Mills theory for families of 4-dimensional manifolds, and used them to examine the topology and geometry of such families. One of typical objects studied using gauge theory for families is the space consisting of all symmetries of a given 4-dimensional manifold. The space of symmetries is a natural mathematical object, but at the same time, this space is an infinite-dimensional complicated space in general, and consequently quite hard to attack. Interestingly, some of my recent work with several groups revealed that we can extract information about the space of symmetries of some 4-dimensional manifolds using gauge theory for families. I am trying to go ahead with this direction, and also to develop other aspects of gauge theory, relating to a sort of topological quantum field theory.
Rigidity of the mod 2 families Seiberg-Witten invariants and topology of families of spin 4-manifolds