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 | Leave a comment

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 | 6 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 | 11 Comments