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