Peng Zhou

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2025-02-26

The 3d GMW theory.

In Kapranov-Kontsevich-Soibelmann paper, 10 years ago, they mentioned that it is possible to consider marked polytope in $\R^3$. There is a $E_3$-algebra controlling the deformation of $E_2$-algebra, and there can be coefficient enhancing all these. I want to understand what precisely is the statement.

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2025-01-23

  • Discussion with Xin Jin about her proof

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2025-01-21

I was discussing with Yixuan yesterday. He mentioned a few works by Siu-Cheong Lau are noteworthy.

  • Localized mirror functor. No, not just probing the space using a compact immersed Lagrangian, but with deformation, allowing immersed Lagrangians.
  • Nakajima quiver variety coming from Floer theory

What is the Crane-Frenkel 4d TQFT? What is the small quantum group? Why we need to be small? Just so the Verma can be defined?

2025-01-15

I have been thinking about Liouville sector. The condition on stop is very harsh, in the sense that the Liouville flow need to preserve the boundary. I am not sure if GPS themselves constructed these required structures.

  • Construct Liouville structure?
  • Examples

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2025-01-09

  • colimit of algebras

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2025-01-07

  • Mina relates Cherns-Simon's partition function $CS(\Sigma \times S^1)$ with our rank of $K$-theory formula.
  • Lecture note on Ringel-Hall algebra.

2025-01-06

We had a long detour into Cautis-Kamnitzer's constructions, at least we had some familiarity with flag variety.

But, I still do not know about disk with 3 or more stops.

  • Disk with 2 stops and $k$-strands, is assigned to $D-mod(pt/GL(k) )$ which is derived equivalent to $NH_k-Mod$.
  • Disk with 2 stops, goes to the monoidal category $U_-$.
  • Disk with 3 stops with $k$ strands, we have $k+1$ many objects serving as generators, and they form an full exceptional collection.

2025-01-05

Today, I did

  1. more study on the slices of affine Grassmannian
  2. Return to CKL

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blog/start.txt · Last modified: 2023/07/16 17:08 by pzhou