# Differential Geometry

Differential geometry is for many reason a very important branch of matematics and has many uses throughout physics.

I have tried to learn it well many times but every time I have met some kind of obstacle in the form of hard concepts or time available.

I am now again trying to learn the subject together with Lie and representation theory in order for me to better understand QFT and modern physics.

## Current challenges

- Differential forms vs covectors
- why the alternating structure for differential forms
- are there other forms than the ones representable as differential forms
- if not, why is there not also an alternating structure on the tangent spaces and only on the cotangent spaces