Appropriate maths for QFT, LQG, strings etc.

[jdstokes]

Hi all,

I asked about this on the academic and career guidance forum but didn't get any useful replies.

Which of these maths subjects (all at fourth year level) would you recommend for someone interested in the subjects listed in the title? What would you say is missing from this list?

Functional analysis
Partial differential equations
Algebraic topology
Algebraic geometry
Commutative algebra
Representations of the symmetric group

http://www.maths.usyd.edu.au/u/UG/HM/pure2007.pdf

By the time I reach fourth year I will have taken courses in metric spaces (topology), rings fields and Galois theory, differential geometry and Lagrangian and Hamiltonian dynamics (applied maths).

Thanks

James

 

[marcus]

...
Which of these maths subjects (all at fourth year level) would you recommend for someone interested in [non-string quantum gravity]? ...

Functional analysis
...
...

http://www.maths.usyd.edu.au/u/UG/HM/pure2007.pdf

Your PDF handbook for the honors program says

The “core" of Fourth Year is considered to include Commutative Algebra, Functional Analysis and Algebraic Topology. ... Students are strongly
advised to take all of the core courses.

1.3. Pure Mathematics 4/PG Courses for 2007
SEMESTER I
Algebraic Topology Paunescu
Commutative Algebra Lehrer (weeks 1-6)
Functional Analysis Dancer
SEMESTER II
Algebraic Geometry Lai
Commutative Algebra Lehrer (weeks 1-7)
Partial Differential Equations Daners
Representations of the Symmetric Groups Molev

If you are unsure about the combination of courses you should take, consult
with your supervisor

They tell you to take the core courses----Alg.Top, Funct.An, Commut.Alg.

That is already a big load. All three are part of a general math education. All three would be valuable preparation for LQG (a cluster of non-string approaches to a fundamental theory of geometry and matter).

Also in the second semester you will be doing the HONORS ESSAY based on a kind of quicky research project with an advisor of your choice. Doing research, working with an advisor, giving a talk---this is very important experience where you learn the ropes and if you are interested in the problem it almost doesn't matter what field it is in. the process of writing a thesis is what you are learning.

I would say take the three core courses---and start thinking "If my interest is in non-string QG, then who should I get for my Honors Thesis research advisor?"

And whoever you decide you want to work with will probably tell you other courses to take----or may likely have ideas along those lines.
================

Are you in Sydney NOW?
The GRG conference is happening this month July 2007.

If you are interested in non-string QG, you should hear the talks of Laurent Freidel and Renate Loll.

Freidel is from Perimeter Institute (ontario province, Canada) which is the most active or one of the two or three most active centers of QG research in the world. He is one of the top people in the LQG community---specialty is spinfoam model of geometry and matter.
Loll is from Utrecht Inst.Theor.Phys. She leads an approach to QG which is NOT part of the LQG cluster, it is simplicial gravity where you put random assemblages of tetrahedra into a computer and have them evolve, shift around, grow and change according to some simple rules that apply at microscopic level, so you get these montecarlo computer simulations of little universes, and you study them and compile statistics about their behavior. She got some stunning results in 2004-2005 and it put this approach on the map. The question is what has her team accomplished in the past year, 2006-2007.

So I advise you go to GRG in Sydney. Freidel will give you a good idea of how it is going in LQG, and Loll will give you a window on the NON-LQG part of the quantum gravity research effort. It is good to be introduced to both.

 

[jdstokes]

Hi marcus,

Thanks for replying.

Yes I live in Sydney. Actually, I just returned from a conference in Queensland on complex systems.

I'm not seriously considering pure maths honours at the moment since I intend to go down the PhD physics route so Physics honours is mandatory.

I'm not registered for that relativity conference (I actually tried asking them for money a few months ago but never got a reply) but do you think I will be able to sneak into any of the lectures?

I missed all of today's talks but I might see if I can attend Kip's public lecture or something when I go into Uni tomorrow. Any recommendations?

PS I had a look at the list of participant talks and couldn't find either of those names you mentioned.

James

 

[marcus]

...
...do you think I will be able to sneak into any of the lectures?
...

PS I had a look at the list of participant talks and couldn't find either of those names you mentioned.

James

you are a local student and at some conferences local students get into listen free

you should ask. several PF people are attending the conference,

BEN! KEA! any advice for this Sydney physics student?

it is kind of late to be asking now the conference has started

==========

It is strange you didnt find Laurent Freidel and Renate Loll named in the program since a little while back they were listed as INVITED PLENARY SPEAKERS. they were programmed as main speakers, so could they both have canceled their talks? not likely.
I don't have time to check the program for you, so must just wish you luck.

 

[marcus]

your original question
You gave a link for the handbook for the math honors program and didnt say you were actually doing physics honors.
So my answer is, for non-string QG, take functional analysis and algebraic topology.

functional analysis will help you with the LQG uniqueness theorem
Lewandowski, Okolow, Sahlmann, Thiemann
and algebraic topology will prepare for the directions people like John Baez and Derek Wise are moving---check their papers on arxiv.

but mainly, focus on your physics honors and do a superb job

 

[jdstokes]

Hi marcus,

Thanks for your useful comments.

You were right about those authors. I was looking at the scientific program rather than the plenary speakers (doh!).

Too bad I missed Friedel's lecture yesterday. I emailed the conference organizers asking if they'd allow me to sit in on Loll's talk or any others. Hopefully they'll say yes or I might just sneak in. From my conference experience they only check for IDs on the first day anyway.


Thanks

James