### Hyperbolic surfaces as singular flat surfaces

Geometry and Topology Seminar

27th October 2020, 2:00 pm – 3:00 pm

Zoom seminar, if interested, please email one of the organisers to gain access to the Zoom link

Hyperbolic surfaces and flat surfaces look very different, but they're

linked by a remarkable correspondence. I'll show you two versions of it:

a geometric "collapsing" process that flattens hyperbolic surfaces, and

a representation-theoretic "abelianization" process that diagonalizes

SL(2,R) local systems. If there's time, I'll mention two related links

between hyperbolic and flat surfaces: one involving the analysis of

harmonic maps, and another involving the dynamics of geodesic flows.

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