# February 9, 2010

## Plan

I plan to write something on three topics:

1. **Several basic spectrum for noncommutative ring and how do them come into the story of representation theory of reductive Lie algebra.**

I will do some explicit computations. The motivation for me is for the research topic course which is now given by A.Rosenberg.I want to understand all of them in detail.

2. **I will start with Zariski topology in commutative algebraic geometry and try to do direct imitation for noncommutative ring.**

Unfortunately, one will find direct imitation failed. Therefore, anotherÂ appropriate topology for noncommutative algebraic geometry will be formulated.After finish it, I will go to the purely functorial point of view to algebraic geometry. I might restrict myself to commutative algebraic geometry.

3. **D-module theory and Lie algebra and their quantum analogue**

I will talk about how noncommutative algebraic geometry naturally comes into the life of D-modules. I will push myself to write localization theory for category of D-modules in almost full details.

Bryan said,

February 16, 2010 at 3:50 pm

Number 2 sounds particularly good(of course the others will be interesting), I can’t wait!

noncommutativeag said,

February 17, 2010 at 4:22 pm

Because now we are revising the spectral theory. I will elaborate a bit.