### About this blog

Rigorous trivialities is a web log about mathematics, but especially geometry, broadly construed. Contributors will be Charles Siegel, Jim Stankewicz and occasionally Matt Deland. Charles specializes in algebraic geometry, topology and mathematical physics. Jim specializes in arithmetic algebraic geometry. Matt has transitioned from algebraic geometry to work in industry.

Header is taken from the larger work by fdecomite under the creative commons license.

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# Category Archives: Uncategorized

## Quasiconformal Maps

Ok, time to get back to Riemann surfaces! We’ve been all about hyperbolic surfaces, and so first let’s compare the two of them: every oriented hyperbolic surface is a Riemann surface, and the conformal class of a complex structure contains … Continue reading

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3 Comments

## Quadratic Differentials

We’re going to get to quasi-conformal maps soon, but first, we’re going to want to build some new objects on our Riemann surfaces. Differential forms are a fairly standard thing, and asserting that they’re holomorphic isn’t exactly a revolution. On … Continue reading

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## Mapping Class Group Elements

Let’s get into the mapping class group and talk a bit about its elements and its structure. I’m going to omit proofs, because I can’t beat Minsky’s exposition, and this is just some flavor and definitions, most of which won’t … Continue reading

## The Mapping Class Group

Last time, we touched on the mapping class group, so now, we’re going to dig in. Now, we’re not going to dig too deeply, there’s a LOT here (see the wonderful book by Farb and Margalit for a hint at … Continue reading

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## Fenchel-Nielsen Coordinates

Welcome back, and hope all you readers had a good 2014 and particularly good holidays and new year’s celebrations, if you do those things. Today, we’re going to keep on the road to producing the moduli space of curves, by … Continue reading

## Hyperbolic Surfaces

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

Posted in Uncategorized
Tagged hyperbolic geometry, hyperbolic surfaces, teichmüller space
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## 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. So we’re going to start by talking a bit about hyperbolic … Continue reading

## New Series: Moduli of Riemann Surfaces

Though I’m not quite ready to start (next week!) I feel that, in the spirit of Jim getting back to the blogging and my continued promises, I’d announce my series now. I’m going to start a detailed series on the … Continue reading

## The torsion on CM elliptic curves over prime degree number fields

It’s good to be back! This weekend I’m going to Paris to give a talk in the London-Paris Number Theory seminar so I’m going to give a preview of that talk, based on joint work with Pete Clark and Abbey Bourdon. … Continue reading

Posted in Uncategorized
Tagged Bourdon, Clark, complex multiplication, elliptic curves, preprint
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## I know I’ve said it before, but…

Rigorous Trivialities will be returning! Not immediately, but it will be. I’m reorganizing a bit, and as I’m going to be contributing to a blog for the general public via the Kavli Foundation, I’m also going to try to revive … Continue reading

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