813 reputation
113
bio website joshphysics.com
location Los Angeles
age 28
visits member for 1 year, 6 months
seen Jul 18 at 3:02

My new website: joshphysics.com

Currently a visiting lecturer at the UCLA Department of Physics and Astronomy.

Ph.D. theoretical high energy physics from UCLA.

BA/BS in physics/math respectively from UC Berkeley.


Feb
8
answered Disprove a linear mapping
Feb
8
asked Cochains: terminology
Feb
7
comment Translations in two dimensions - Group theory
@user35952 Unfortunately I think not.
Feb
7
comment Translations in two dimensions - Group theory
@user35952 Yes it's a circle too. It's a circle with the same radius but whose center is at $(-a,-b)$. We could only have said that the equation for the circle was preserved in form (at least if we're using standard terminology) if there were some $R$, say, for which the transformed equation were $x^2+y^2 = R^2$; that equation has the same form. So, for example, a scaling $x\mapsto \alpha x, y\mapsto\alpha y$ would preserve the form of the equation for a circle at the origin because the new equation would be $x^2 + y^2 = (r/\alpha)^2$. Are thinking of a different notion of "preserve."
Feb
7
comment Translations in two dimensions - Group theory
@user35952 Well let's see. A circle is described by the equation $x^2 + y^2 = r^2$, and if we translate $x\mapsto x+a$, $y\mapsto y+b$, then we get $(x+a)^2 + (y+b)^2 = r^2$ which is certainly not an equation of the same form. In fact, the only such equation that will have the same form is the equation for any line in the direction of the translation $(a,b)$ itself.
Feb
7
comment Translations in two dimensions - Group theory
+1: I had forgotten about this way of packaging things; very slick.
Feb
7
comment Translations in two dimensions - Group theory
@user35952 I don't quite understand what you mean. Could you be more specific about what sorts of "equations" you're referring to?
Feb
7
answered Translations in two dimensions - Group theory
Feb
6
comment Intuition for chains and cochains
@AymanHourieh I actually have the first book; didn't think to look there. What I'd really like to read is some sort of exposition devoted entirely to the intuition. Perhaps something that does computations in the context of some physical applications of chains and cochains with lots of pictures etc. I feel like someone somewhere must have written something like this. Thanks for the references.
Feb
6
comment Intuition for chains and cochains
@AymanHourieh I don't know enough about cohomology to answer the first question, but I suspect I'd be interest in all of the above on some level. I've worked through most of Spivak's Calculus on Manifolds, I've learned a decent amount of differential geometry in the context of general relativity and high energy physics, I'm comfortable with differential forms, covariant derivatives, etc. (although I imagine understanding semi-Riemannian geometry won't really help much here)
Feb
6
comment Intuition for chains and cochains
Thanks. I'll check it out.
Feb
6
asked Intuition for chains and cochains
Feb
6
comment If differential 1-forms agree on chains with integer coefficients, are they equal?
Thanks; that's a nice argument.
Feb
5
comment If differential 1-forms agree on chains with integer coefficients, are they equal?
@BrunoJoyal Ah interesting ok. I need to learn what the universal cover is, but thanks.
Feb
5
comment If differential 1-forms agree on chains with integer coefficients, are they equal?
@BrunoJoyal Haha ok thanks. I was just so confused; I went back to "Calculus on Manifolds" to make sure I wasn't going crazy. So the original result I wrote is true, regardless of topology? If so, is there a simple proof?
Feb
5
comment If differential 1-forms agree on chains with integer coefficients, are they equal?
@BrunoJoyal I am not so familiar with cohomology; if I restrict the topology of the manifold in some way, can I ensure that they are equal?
Feb
5
asked If differential 1-forms agree on chains with integer coefficients, are they equal?
Feb
4
comment Chains and cochains: integer versus real coefficients
@MartianInvader Well then. That's rather embarrassing. Thanks.
Feb
4
asked Chains and cochains: integer versus real coefficients
Feb
1
comment Representation of a group
@Dilaton The close votes are to move this question to math.SE because this is a purely mathematical question. There are certainly physical consequences of this stuff, but the OP does not ask about physics in the question.