Thread: Exciting Research Areas...

Hi guys & girls,

I was wondering if any of you could please help me?

Now that I am reaching the end of my masters in mathematics I need to start thinking about what I might do a PhD in. I absolutely love analysis! Particularly classical analysis - I could sit differentiating, integrating & looking at infinite series & limits until the cows come home! :-D

I also have a great fondness for topology. :-)

I was wondering if anyone could please shed some light on some specific exciting research areas that they think might "light my fire" so to speak? :-D

Many thanks x

PS - I'm also really into physics - especially of the theoretical variety. I've done courses on quantum, S & G relativity, and Newtonian, Lagrangian & Hamiltonian mechanics whilst at uni, as well as ones in topology, analysis, complex analysis, elliptic functions, algebraic topology, differential geometry, etc. Are there any research areas that would also incorporate these too? One of my friends said Algebraic Geometry & Morse Theory might be worth looking into...? Some one else said that there are links between algebraic topology & quantum-y stuff....? Another said I wont really encounter any classical analysis unless I do research analytic number theory - is that true?

Many thanks again - I eagerly await any advice or ideas you may have! :-) x

PPS - I am also FASCINATED by rigor and logic - I have always been far more interested in the proofs than I have the actual results!

I've always wanted to really understand how all of maths and physics works.

But sadly I've been unable to do any logic or set theory courses at my uni as an undergraduate. :-( x

PPPS - David Hilbert is my biggest source of inspiration - "physics is too hard for physicists!" :-D x