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Tea time：15:30, Room 707
Abstract:
The space of simple closed curves on a surface of finite-type happens to be more complex than many expected. The compactification, space of measured laminations, and the simplicial complex point of view, the curve complex, both happen to contain rich stories in them. In this talk, I will start with the moduli space of flat tori and the moduli space of hyperbolic surfaces, i.e., Riemann surfaces. The dynamical viewpoint and the metric viewpoint of the moduli space led to the study of quadratic differentials. The main goal of the talk will be to introduce flat surfaces, discuss intuitive and counter-intuitive properties, and set up a few possible future directions. In particular, I will illustrate examples of length rigidity problem: whether the lengths of a set of curves determine the metric. This talk only assume basic intuition regarding curves and surfaces, but an understanding of hyperbolic geometry or Riemann surfaces will be helpful.
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