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NCTS Differential Geometry Seminar
 
16:00 - 17:00, October 5, 2017 (Thursday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Rigidity of Length Functions for Flat Surfaces
Ser-Wei Fu (National Taiwan University)

Abstract

The spectrum of geodesic lengths is known to contain useful information when considering non-positively curved manifolds. In particular, a hyperbolic surface is uniquely determined by the length function of a set of chosen geodesics. We are interested in analogous results for non-positively curved closed surfaces.

In this talk, I will start with the story of Riemann surfaces, hyperbolic surfaces, and classical length rigidity results. Flat surfaces arise naturally in the study of moduli spaces and lie in the intersection of multiple disciplines. The goal is to introduce both rigidity and non-rigidity type results regarding flat surfaces. I will use the torus to illustrate the concept and discuss the tools required in the general case.



 

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