Ok, with the hyperbolic plane and its metric and geodesics out of the way, we can start getting into some surface theory. 583 more words

## Tags » Hyperbolic Geometry

#### The hyperbolic plane

So, I know I usually talk about strictly algebraic geometry stuff, but the moduli of curves lives in an interesting place. It’s both an algebraic and an analytic object. 394 more words

#### Mapping class groups: the next generation

Nothing stands still except in our memory.

- Phillipa Pearce, *Tom’s Midnight Garden*

In mathematics we are always putting new wine in old bottles. No mathematical object, no matter how simple or familiar, does not have some surprises in store.

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