Introduction to Alexandrov geometry and Degenerations of geometric objects
The goal of this course is to present two theories about degenerations of spaces in geometry. In the first part, we introduce Alexandrov Geometry. In differential geometry, being positively or negatively curved is defined in terms of inequalities satisfied by the coefficients of the curvature tensor. However, riemannian manifolds can degenerate to objects that do not keep a manifold structure. Alexandrov geometry is about giving a meaning to curvature inequalities in the general settings of metric spaces.
In the second part, we will discuss translation structures as examples of flat metrics with conical singularities and present the various compactification theories for their moduli spaces. If time allows, we will also discuss degenerations of complex affine structures with the recent proof of the existence of closed geodesics in dilation surfaces.
In the second part, we will discuss translation structures as examples of flat metrics with conical singularities and present the various compactification theories for their moduli spaces. If time allows, we will also discuss degenerations of complex affine structures with the recent proof of the existence of closed geodesics in dilation surfaces.
讲师
日期
2024年10月08日 至 12月25日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周三 | 10:40 - 12:15 | Online | ZOOM 14 | 712 322 9571 | BIMSA |
修课要求
Basic Differential Geometry and Complex Analysis
课程大纲
Part 1: Alexandrov Geometry
1) Gromov-Hausdorff convergence of metric spaces
2) CAT(0) spaces
3) Dimension theory for CAT and CBB spaces
4) Gradient Flow
Part2 : Geometric structures on surfaces
1) Introduction to the flat geometry of translation surfaces
2) A flat geometric picture: The WYSWYG compactification of strata of meromorphic differentials
3) An algebro-geometric picture: The Multi-scale compactification of strata of meromorphic differentials
4) Degenerations of complex affine structures: proving the existence of closed geodesics in dilation surfaces
1) Gromov-Hausdorff convergence of metric spaces
2) CAT(0) spaces
3) Dimension theory for CAT and CBB spaces
4) Gradient Flow
Part2 : Geometric structures on surfaces
1) Introduction to the flat geometry of translation surfaces
2) A flat geometric picture: The WYSWYG compactification of strata of meromorphic differentials
3) An algebro-geometric picture: The Multi-scale compactification of strata of meromorphic differentials
4) Degenerations of complex affine structures: proving the existence of closed geodesics in dilation surfaces
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Tahar是BIMSA助理研究员。在加入BIMSA之前，他曾在魏茨曼科学研究所担任高级博士后研究员。他致力于平面上各种几何结构的模空间研究，包括平移和扩张结构、平坦度规和锥球度规。Guillaume-Tahar最近的研究兴趣涉及线性微分算子、isoresidual fibrations和simplicial arrangements of lines.