# Possible directions in noncommutative geometry

I recently came across noncommutative geometry and found it rather interesting. I should mention that I'm a graduate student considering options for my research and if I were to name an area which I'm interested in, then it would be functional analysis including operator algebras etc., and that was how I got to know about noncommutative geometry. From what I've been told, noncommutative geometry is a very broad area so I would think that one can go in many different directions after entering the field. What I would like to find out is what some of these directions are. Also, if I am to go into this field, my motivation will probably be functional analytic so I will be particularly interested to know if there is an approach that suits me.

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Please read: mathoverflow.net/howtoask To be more positive: don't you have in your department a professor / post-doc / more advanced PhD student with whom you could discuss this (rather vague) question over coffee? – Alain Valette Apr 21 '13 at 16:40
i think so but I being a newbie myself I couldn't resist to pour my knowledge over – Koushik Apr 21 '13 at 16:49
This should probably be community wiki, as you are asking for a list, rather than a single correct answer. You also accepted an answer pretty quickly! – MTS Apr 21 '13 at 20:37

it's my personal opinion but I think the second approach may go a long way in the future.the heart of the approach is "arveson conjecture" which relates homogeneous varieties in the unit ball of $C^n$ with essential normality of d-shift operators vaguely – Koushik Apr 21 '13 at 16:47