### 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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### Top Posts & Pages

- AG from the Beginning
- I know I've said it before, but...
- New Series: Moduli of Riemann Surfaces
- The Chow Ring and Chern Classes
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- Locally Free Sheaves and Vector Bundles
- Line Bundles and the Picard Group
- Geometric Form of Riemann-Roch
- Tangent Spaces and Singular Points

# Monthly Archives: October 2007

## Ricci Flow on Surfaces of High Genus

I’ve been a bit busy lately, and so I missed last week posting. So what I’ve decided to do is to take the talks I’ve given in various graduate student seminars over the last year or so and convert them … Continue reading

Posted in Differential Geometry
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## Hamiltonian Mechanics

Hi everybody, Well, I’m finally getting around to talking about the Hamiltonian formalism of classical mechanics. Of course, if you’ve been keeping up with The Everything Seminar, the good people over there have discussed this very topic recently (with some … Continue reading

Posted in Mathematical Physics
5 Comments

## Introduction to Symplectic Topology

Hi everybody, In my last post, I promised that I would talk about the Hamiltonian and Lagrangian formalism of classical mechanics. In order to do that, we need to first develop some topological ideas, specifically in the area of symplectic … Continue reading

Posted in Mathematical Physics
5 Comments

## Elliptic Curves

So, on Thursday, I posted some background stuff, which I think I might continue to do in the future. Just in general if I want to do a real post which there’s some basic technical stuff that needs to be … Continue reading

Posted in Algebraic Geometry
5 Comments

## Locally Ringed Spaces and Varieties

Ok, I’m writing this now specifically so that I don’t have to do it in my Monday post, because I need it to even define what I’m talking about. Today’s topic of interest are locally ringed spaces, and they are … Continue reading

Posted in Algebraic Geometry
4 Comments

## Geometry of a Polynomial

This week, we’re going to talk about some of the more important ideas in algebraic geometry, and in particular we will be picking a polynomial and describing its geometry in detail. This polynomial is not taken at random in any … Continue reading

Posted in Algebraic Geometry
1 Comment

## Newtonian Mechanics

Hi everybody, I was thinking that I would do a series of posts about classical mechanics from a mathematician’s standpoint. This post will be an overview of the Newtonian formalism of the subject, with some important examples so the usual … Continue reading

Posted in Mathematical Physics
8 Comments