Good research areas in pure math

[Shabani makwaru]

My name is shabani makwaru from Tanzania i am master student in Pure mathematics at University of Dar es salaam Please can help me in advising which area is good in research in pure math

 

[fresh_42]

Define "good"! This is a personal assessment, so how can we know what you consider good or bad?

 

[Shabani makwaru]

yes off course is personal assessment I want to know research areas which are not too difficult to complete dissertation

 

[fresh_42]

I have a rather simple, but as far as I know, new idea. However, I don't know what it's worth. It's about Lie algebras. I once hoped to shine some light into the classification of non semisimple Lie algebras but I haven't found a good key. Only many, but none of which opened actually some interesting doors. I still don't know whether I wasn't able to see the interesting stuff or whether there was none.

But you see, this answer depends on how you like Lie algebras, the algebraic part, not the analytical, although I suspect there is one, too. Hence I will have to ask: in which area are you searching for an answer. Pure mathematics is still very broad,

 

[Shabani makwaru]

Thanks a lot for your contribution in my country Pure mathematics in graduate studies is new field till now we have less than 30 Phd (supervisors) most of them are functional analysis expert and linear algebra so I need to know much on those two areas

 

[fresh_42]

Well, the algebraic part of Lie algebra theory is linear algebra, as they are subalgebras of the general linear algebra. I don't know enough about functional analysis, so I cannot answer this part. To me it is a giant mess of pits, traps and slings: several concepts of convergence, theorems which no longer hold in the infinite dimensional case, the wild mixture of measure theory, topology and analysis; and you have to be cautious with any intuition, since chances are you are wrong.

There does exist a connection between the two fields you mentioned: algebras of differential operators. I guess - but it is a guess - that there are still many open mathematical questions in string theory.