Geometric structures on surfaces
In this course, we give a panorama of geometric structures a topological surface can be endowed with. We will discuss combinatorial decompositions, natural dynamical systems and moduli spaces of these structures. We will focus on geometric structures compatible with a structure of Riemann surface (translation structures, dilation structures, cone spherical metrics...).
讲师
日期
2023年03月28日 至 06月13日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周二 | 14:20 - 16:05 | A3-2a-202 | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
Undergraduate general topology and complex analysis
课程大纲
Part I: Simplicial structures and Polyhedra
Part II: Basic theory of Riemann surfaces
Part III: Introduction to Translation surfaces
Part IV: Geometry of meromorphic differentials
Part V: A flat illustration of Morse Theory on surfaces
Part VI: Walls-and-chamber structures on strata of meromorphic differentials, Veech groups
Part VII: Isoresidual fibration and Mittag-Leffler theorem
Part VIII: Quadratic differentials, half-translation surfaces and cone spherical metrics with special monodromy
Part IX: Geometry of the moduli spaces of cone spherical metrics
If there is enough time, we will also discuss dilation and complex affine structures.
Part II: Basic theory of Riemann surfaces
Part III: Introduction to Translation surfaces
Part IV: Geometry of meromorphic differentials
Part V: A flat illustration of Morse Theory on surfaces
Part VI: Walls-and-chamber structures on strata of meromorphic differentials, Veech groups
Part VII: Isoresidual fibration and Mittag-Leffler theorem
Part VIII: Quadratic differentials, half-translation surfaces and cone spherical metrics with special monodromy
Part IX: Geometry of the moduli spaces of cone spherical metrics
If there is enough time, we will also discuss dilation and complex affine structures.
参考资料
Donaldson: Riemann Surfaces
Zorich: Flat Surfaces
Zorich: Flat Surfaces
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
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.