Workshop on holomorphic neighborhoods of compact manifolds and CR geometry

Schedule　(PDF)

Monday, December 15th
10:00–10:50 Xiaojun Wu (Osaka Metropolitan University)
Some Remarks on the Formal Principle for Line Bundles
In this talk I will discuss conditions under which a formal isomorphism of line bundles along a compact complex submanifold extends from the formal neighborhood to an analytic neighborhood. Building on a recent paper of Koike, who treated the case where the ambient space admits a compact Kähler compactification, I will show that his arguments extend to some more general settings under suitable cohomological assumptions. After reviewing the relevant parts of Koike’s work, I will present applications to nilmanifolds, toric manifolds, and certain examples in the Fujiki class.
11:00–11:30 Yangyang Zhang (Osaka Metropolitan University)
TBA
13:30–15:30 Informal Discussion
16:00–16:50 Maxime Chatal (Kyushu University)
Real almost reducibility of quasiperiodic cocycles
Reducibility and almost reducibility of quasiperiodic cocycles are key properties for understanding their dynamical behavior. Reducibility means that a cocycle can be conjugated to a constant one, while almost reducibility means that it can be conjugated arbitrarily close to a constant cocycle. This talk examines whether an infinitely differentiable almost reducible real cocycle can be almost reduced to a real constant cocycle through real conjugations.

Registration

Talks other than the informal discussion will be streamed online via Zoom. For online participation, please register by December 14th at this form. The zoom link will be sent in the morning of December 15th. For onsite participation, no pre-registration is needed.

Organizers

Acknowledgement

This workshop is supported by JSPS MEAE-MESRI Sakura program (PI: Takayuki Koike and Laurent Stolovitch) and Osaka Central Advanced Mathematical Institute (OCAMI) Joint Usage/Research FY2025 (general) (C) “Holomorphic neighborhoods of compact manifolds and CR geometry” (PI: Masanori Adachi).