Peng Zhou

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blog:2023-06-21

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2023-06-21

I don't like the feeling of 'having to do something', such as, writing this paper. I need to persuade myself again and again to write it. The only reason that I have is, I need to write this paper, so I am done with it. That's not a good feeling.

Andrei is saying, writing paper is not a waste of time. The process of telling a coherent story forces one to think better and express better. So, here I am.

I think the obstacle for me to write anything is a lack of 'actionable' plan. I don't like the word of 'actionable', maybe call it 'executable'. Let me think about what I need to do here.

The need to talk

The Geometry of Coulomb branch

We have a clear understanding of what this space is and what this superpotential is. I just need to explain it.

  • We have the definition of Coulomb branch from BFN, which is about the spec of a convolution algebra. We also have the superpotential.
  • We want to understand the fiber of the algebraic integrable system. There are two tricks
    • abelianization, we write the Coulomb branch as cotangent bundle of the dual Cartan torus mod Weyl
    • compactification, we glue two copies, and do affinization.
blog/2023-06-21.1687370854.txt.gz · Last modified: 2023/06/25 15:53 (external edit)