Pure math in astrophysics-Suggestions needed

[geor]

pure math in astronomy-astrophysics.Suggestions needed

Hello,
I am an undergraduate student of mathematics, and I'm interested in
astrophysics-in a level of watching documentaries (no scientific knowledge).
I want to have graduate studies, I like the idea of astronomy-astrophysics
(even though I don't have a clue- but that's how usually people start, isn't it?),
but I would also like to study pure mathematics.Anyway, my question is which branches of pure mathematics can be needed in astrophysics.Thanks!

 

[chroot]

Honestly there really isn't a lot of higher-level pure math in astrophysics proper. You might find some uses for group theory or algebra if you get into writing or optimizing codes (computer programs) for simulations. Analysis won't matter, since astrophysicists really aren't concerned with the way numbers are constructed. Algebra won't matter, since you're not really concerned with any formal logic. You might find a few applications of the conclusions of geometric topology here and there. You'd definitely find many applications of tensor calculus.

In general, though, I don't think you're going to find much pure math in astrophysics. I am not, however, an astrophysicist, so perhaps someone else can give a more reliable answer.

- Warren

 

[Stingray]

I agree that those things traditionally studied by people in astronomy departments don't involve any pure math at all.

But there are very mathematical investigations into the implications of general relativity. There's a lot of room for differential geometry, heavy-duty PDE theory, etc. Look up people like S. Klainerman, D. Christodoulu, or Y. Choquet-Bruhat. I don't know if you'd consider their work to be astrophysics (most wouldn't).

But regardless, there are only a handful of people doing this sort of thing. "Real" mathematics is almost completely unknown to the vast majority of working physicists.

 

[Gokul43201]

There's a small but active community of mathematicians that specialize in GR and related aspects of astrophysics (some would prefer to call them mathematical physicists).

One such person works in the building across the street from here: http://www.math.ohio-state.edu/~gerlach/

 

[chroot]

I guess the point is that GR is not really considered "astrophysics," even though nearly all of the tests of GR to date have involved astronomical systems. Oddly enough, "astrophysics" seems to be a label that is only applied to experimentalists who conduct "astronomical" experiments.

- Warren

 

[Gokul43201]

Oddly enough, "astrophysics" seems to be a label that is only applied to experimentalists who conduct "astronomical" experiments.

- Warren

Actually, in most physics departments (from my experience), it's the other way round - they are more likely to have a theoretical astrophysics group than an experimental group. The experimentalists typically get labeled as astronomers (in schools where there are separate departments for physics and astronomy).

 

[Philbin]

I guess the point is that GR is not really considered "astrophysics," even though nearly all of the tests of GR to date have involved astronomical systems. Oddly enough, "astrophysics" seems to be a label that is only applied to experimentalists who conduct "astronomical" experiments.

- Warren

Eh? Astrophysics is traditionally divided into "observational" (only rarely called "experimental", and that generally by outsiders; with the exception of a relatively few people who do things like measuring spectra and nuclear properties and such in the lab, for comparison to observations) and "theoretical", plus some "instrumentation" (also occasionally called "experimental"). Theory is part and parcel of astrophysics; indeed, the line is probably more blurred than in other areas of physics, as many (but not all) "observers" do computational work, and many (but not all) "theorists" work directly with observational data.

As for GR, there are a great many relativists whose work is classified under "astrophysics"; in particular, the ones who do numerical work. My institution, for example, has one of the foremost numerical relativists, whose group works on neutron star collapse, binary mergers, and such, in addition to more "pure" GR work such as predicting results of direct tests of GR like Gravity Probe B.

 

[chroot]

Ah, well, mea culpa. Like I said, I'm not an astrophysicist.

- Warren

 

[Stingray]

As for GR, there are a great many relativists whose work is classified under "astrophysics"; in particular, the ones who do numerical work. My institution, for example, has one of the foremost numerical relativists, whose group works on neutron star collapse, binary mergers, and such, in addition to more "pure" GR work such as predicting results of direct tests of GR like Gravity Probe B.

True, but these sorts of people are not using the methods of a mathematician in any way. So they don't fit what the OP was asking about.

 

[Philbin]

True, but these sorts of people are not using the methods of a mathematician in any way. So they don't fit what the OP was asking about.

Indeed, but this wasn't addressed to the OP.

However, there certainly is interaction between the numerical folks and the pure theorists. What the "mathematical physicists" and such come up with in GR generally winds up being tested via astrophysics. I don't argue at all, though, that the people doing "pure mathematics" with direct astrophysical applications are few, if any.

(Now, there are people who call themselves mathematicians who work on string theory and M theory and all that, and perhaps are in fact doing fundamental mathematics with physics applications, and they do indeed often claim to be working on issues related to black holes or cosmology. But that's pushing the definition of "astrophysics".)

 

[berkeman]

There's a small but active community of mathematicians that specialize in GR and related aspects of astrophysics (some would prefer to call them mathematical physicists).

One such person works in the building across the street from here: http://www.math.ohio-state.edu/~gerlach/

Wow, that was fun, Gokul. I spent some time clicking down through his pages -- makes me want to go back to school for a while..

among others:

Twenty-one reasons why you should take
"Mathematical Principles in Science" (Math 601, 602, 603.02)


In Math 601 you will learn, among others

The mathematics of the states of a linear system (vector space theory)
The mathematics of reference frames and their transformations (bases and the representation theorem)
The mathematics of linear systems (the four fundamental subspaces of amatrix)
The mathematics of covectors and metrics (linear functionals and dual vector space theory)
The mathematics of least squares approximations (subspaces and inner products)
The mathematics of stable and unstable systems (phase portrait of coupled system of differential equations)

 

[geor]

Ok, I got an idea of things.The answer seems to be negative, but I see now that maybe this "pure" in front of "mathematics" made things more complex..What about "applied" mathematics (i.e. computational analysis e.t.c.).How much are they needed in astrophysics and in which branches?

But there are very mathematical investigations into the implications of general relativity. There's a lot of room for differential geometry, heavy-duty PDE theory, etc. Look up people like S. Klainerman, D. Christodoulu, or Y. Choquet-Bruhat.

What about differential Geometry (that's something I like!)?
Also, (I'm not into things so much) who's D. Christodoulu?

Thanks for the link,Gokul, I'll check it out.

 

[Stingray]

Ok, I got an idea of things.The answer seems to be negative, but I see now that maybe this "pure" in front of "mathematics" made things more complex..What about "applied" mathematics (i.e. computational analysis e.t.c.).How much are they needed in astrophysics and in which branches?

Applied math is useful in many ways. Almost every branch of astrophysics involves numerical simulations, and in some cases, computational analysis could be very useful. I recall Jerry Marsden and company making some practical contributions to simulations in magnetohydrodynamics (MHD) using things like symplectic geometry. The people who do simulations usually know very little about serious numerical analysis. Someone who does know a bit about it could be very helpful.

What about differential Geometry (that's something I like!)?
Also, (I'm not into things so much) who's D. Christodoulu?

I don't know specifically what type of differential geometry is useful. By giving those names, I was suggesting that you look up their papers to see if that kind of work is interesting. Sorry I mispelled Christodoulou. Here's his webpage (though it isn't very useful): http://www.math.ethz.ch/~demetri/"

There are also people who are far less mathematically rigorous than the ones I mentioned, but are perhaps still interesting to you. For example, R. Wald, A. Ashtekar. and E. Newman have made many interesting contributions to GR (and other fields). I would label the first group of people I mentioned as basically mathematicians working on problems inspired by physics. But this latter group are definitely physicists in the standard sense. They just have a more rigorous inclination than most theorists.

 

[geor]

Indeed, the page isn't very helpful but Christodoulou is Greek (I'm Greek too) and maybe he knows something about things here in Greece and suggest something.I'll mail him and hope he will answer..
Thanks a lot!