So, I've been very interested recently with the developements of the (now mathematically precise) theory of Coulomb branches - in particular because of its recent applications on representation theory and symplectic geometry.

They have been considered by mathematical physicists for a time, but without a rigorous definition. The first attempt to give such a definition was made by H. Nakajima, *Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories*.

This project was completed by A. Braverma, N. Finkelberg, H. Nakajima in

*Towards a mathematical definition of Coulomb
branches of 3-dimensional N=4 gauge theories, II*, and their companion papers

*Coulomb branches of 3d N=4 quiver gauge theories and slices in the affine Grassmannian. With two appendices by Braverman, Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Nakajima, Ben Webster and Alex Weekes.*

*Ring objects in the equivariant derived Satake category arising from Coulomb branches. Appendix by Gus Lonergan.*

Now, I've become rather convinced that to proceed with my research I need to have a rather firm grasp on the tree papers above by Braverman, Finkelberg and Nakajima.

Now, I unfortunately have no good physics intuition, and I've found that some parts of the above papers are very technical and are motived by a lot of different constructions in geometric representation theory in the range of the past 20 years. The final form of this theory is a remarkable achievement of novel ideas and technical mastery, and I'm feeling a little bit lost on what should be the relevant things to focus on (important previous work and mathematical techiniques and machinery).

Hence, the question: what is the royal road to Coloumb branches?

PS: the two papers I'm trying to fully appreciate are:

J. Kamnitzer, P. Tingley, B. Webster, A. Weekes and O. Yacobi, *On category O
for affine Grassmannian slices and categorified tensor products.*

and

A. Weekes, *Generators of Coulomb branches of quiver gauge theories*, arXiv:1903.07734.