This seminar aims to have research exchanges among the researchers of the
differential geometry,the geometric analysis, topology, algebraic geometry
and its applications.
(This seminar is held as an event of RIST TUS ``Division of Joint Research
of Geometry and Natural Science''.)
2025
・The 1st Kagurazaka Geometry Seminar
Speaker: Yuji Hirota（Azabu University）
Title: Lie algebroid symmetry and generalization of momentum maps
Date: July 12, 2025
Place: Tokyo University of Science, Kagurazaka Campus (Room 222)
Abstract: The theory of momentum maps has been extended and developing in various directions according to a lot of mathematical or physical interests. In general, one supposes a Lie group action in the definition of a momentum map. However, the discovery of Lie algebroid symmetry by C. Blohmann, M. C. Fernandes and A. Weinstein in the early 2010's has increasingly needed to extend the notion of usual momentum maps. Such generalization of a momentum map is called a momentum section.
In this talk, we shall take a brief look at the results of extending momentum
sections defined for (pre)symplectic manifolds to higher symplectic manifolds.
Specifically, we show that quaternionic K\"{a}hler momentum maps by
K. Galicki and H. B. Lawson can be described in our framework. Furthermore,
we show that under suitable conditions, a result similar to the Marsden-Weinstein
reduction theorem in symplectic geometry also holds for the zero locus
of a momentum section.
The talk is based on joint work with Noriaki Ikeda (Ritsumeikan University).
Record of 2002〜2024
Record
Organizer： Naoyuki Koike，Makiko Tanaka，Susume Hirose，Akifumu Sako,
Kurndo Baba，Daisuke Yamakawa, Yasufumi Nitta, Hisanori Ohashi,
Natsumi Oyamaguchi，Toru Kajigaya，Naoki Kimura，Tomoki Fujii