# 微分幾何学セミナー

#### 微分幾何学セミナー（2022年度）

タイトル Deformations of holomorphic-Higgs pair

アブストラクト Let X be a complex manifold and (E,\theta) be a Higgs bundle over X. We study the deformation of holomorphic-Higgs pair (X,E,\theta). We introduce the differential graded Lie algebra (DGLA) which comes from the deformation. We derive the Maurer-Cartan equation which governs the deformation of the holomorphic-Higgs pair, construct the Kuranishi family of it, and prove its local completeness.

タイトル Uniform Hörmander estimates for flat nontrivial line bundles

アブストラクト Hörmander’s L^2-estimates for the dbar operators on holomorphic line bundles are of fundamental importance in complex analytic geometry, whose conventional proof relies on the positivity of the line bundle. In this talk, we prove the L^2-estimates for the solutions to the dbar equation that hold uniformly for all flat nontrivial line bundles on compact Kähler manifolds, whose main feature is the quantitative description of the blow-up behaviour as the line bundle approaches the trivial one. A key ingredient in the proof is the observation that flat line bundles are topologically trivial and can be identified with the trivial bundle with the "perturbed" dbar operator which we define in terms of coordinates on the Picard variety. This is a joint work with Takayuki Koike.

タイトル An isoperimetric inequality, an expansion coefficient and a lower bound for the Cheeger constant of a metric measure space

アブストラクト The present study is intended to demonstrate an isoperimetric inequality in terms of Ledoux's expansion coefficient on a metric measure space with a certain functional inequality; the Ledoux's expansion coefficient gives rise to an exponential concentration. The result enables us to bound the Cheeger constant of the metric measure space from below in terms of the constant attributed to the functional inequality.

タイトル Symplectic methods in the restricted three-body problem and applications

アブストラクト In this talk, I will discuss the well-known restricted three-body problem from the perspective of modern symplectic geometry, as well as applications to the numerical search of orbits within the context of space mission design.