When two layers of a periodic material are rotated relative to one another, a large scale pattern, called a moire pattern, is formed. Although moire patterns have been known in textiles for hundreds of years, it wasn't until 2018 when experiments revealed that twisting two thin layers of a material can dramatically alter its electronic properties. The poster child for new and exciting behavior in moire systems is twisted bilayer graphene (TBG) which can transition between being a conductor to being an insulator simply by changing the twist angle between the layers. In this talk, I will discuss my recent work on mathematically understanding the role of electron-electron interactions in the properties of TBG both from a numerical and a theoretical perspective. In particular, I will discuss our recent result which fully characterizes the ground state manifold of TBG with electron-electron interactions in a simplified limit.