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blog
2023-08-31
So I talked with YX a bit on 'what is the weight grading', in mixed sheaves. It is just the eigenvalue of the Frobenius action, on etale sheaves.
Then, why the endomorphism of the big tilting has that weight grading.
2023-08-30
Let's think about hypertoric variety, Gale duality.
Given a vector space in $\R^N$, we have $$ V \to \R^N \to (V^\perp)^* $$ $$ V^\perp \to (\R^N)^* \to V^* $$ Great. Given $\eta \in (V^\perp)^*$ and $\xi \in V^*$, we look at the fiber $V_\eta$ and $(V^\perp)_\xi$, they are partitioned by the restriction of the sign partitions in $\R^N$ and $(\R^N)^*$.
Feasible is dual to bounded. So the two sides has the same collection of feasible and bounded.
Consider the Lagrangian $(V \oplus V^\perp)_{\eta, \xi}$ intersecting with the diagonal sign blocks in $T^*\R^N$.
I still don't know why we have this correspondence of bounded and feasible chambers. But we do, and the two linear spaces $V$ and $V^\perp$ can be really different.
2023-08-05
- write up the notes that are useful for myself.
- why quiver gauge theory has anything to do with Kac-Moody algebra?
The stuff that I typed up below, are so incoherent and dreamy, that I don't know what am I talking about. So they should be either cleaned up or deleted.
I also cleaned up some to read papers.
I don't think I want to write up the example computation of the spaces.
2023-08-01
academia or not
The application season is coming. But I do not want to apply again. I think I will get rejected again. I will just write papers, write codes, and do stuff for people to make money. That being said, I am free and I am going to work on stuff that I am really interested in.
Today:
- I want to understand the example of why cohomology of dual symplectic resolutions have the same cohomology. Following Kamnitzer's lecture.
- I want to finish writing the superpotential section.
2023-07-31
- obsidian?
2023-07-30
- abelian with matter is the trouble
2023-07-27
- what to say next
2023-07-26
Declaration: I was lost in abstract definitions for too long. I will now compute examples, examples, and examples. Not only because abstraction makes me sleepy, but also examples makes my hands dirty and my mind happy.
- Reading Ginzburg's paper
- Heisenberg algebra and Weyl algebra (just names)
- Writing my own paper
2023-07-25
- problem with torsion in $\pi_1(G)$.
2023-07-24
- reading Chriss-Ginzburg the whole morning
- watched a youtube video 8 traits of successful people
- try to fix the annoying keyboard on a macbook pro, which turns out to be not my (or my wife's) fault.
- found an interesting lecture note of Teleman on rep theory. Never really understood what is character formula.