Complex geometry: When spaces repel functions !
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Pellos - 1R2 207
Riemann surfaces are geometric shapes that can be imagined as deformed spheres or doughnuts. At first sight they may look quite similar, but a simple topological feature -the number of "holes'' they have- turns out to have a remarkable influence on their geometry.
In this talk, we explore how the topology of a Riemann surface shapes the behavior of complex curves drawn on it. While some surfaces happily accommodate many curves, others behave quite differently: their geometry seems to push curves away !
The goal of this talk is to give an intuitive glimpse of this phenomenon and to show how the simple act of adding holes to a surface can dramatically change the geometric world that lives on it. Through pictures and geometric intuition, we will see how topology quietly governs the shapes and curves that a surface allows.