Goal

I must have not updated my blog in such a long time that I got a shock because of the change of the UI for blogspot. This post is intended for me to list down things I want to learn so that I can refer to in the future. So here are the mathematics topics that I would like to learn more about:

• Algebraic Number Theory. I want to learn Local Class Field Theory and Global Class Field Theory
• Analytic Number Theory. I want to have better understanding of L-functions and the related stuff
• Algebraic Geometry. The amount of Algebraic Geometry I know is very superficial and are mostly classical stuff. I think the right way for progress is to work through Hartshorne and survive the Cohomology theories. I think my goal is set on reaching Weil's conjectures and Arithmetic Geometry.
• Algebraic Topology. There are some important concepts imported from Algebraic Topology so I think it is a good idea to look into the root and learn Algebraic Topology.
• Modular Forms. Somehow this ties back to Elliptic Curves. I think it will be a good idea if I have a better understanding of Modular Forms.
• Linear Representation of groups. Number Theory is essentially the study of the Galois group of a fixed algebraic closure of Q. One way to understand it better is via representation theory. I feel that this is an area that I should work upon.

So many projects; so little time.

PS: This is 101st post.