• Reading Teleman

What's the input data? A compact Lie group (what's the difference between this and a complex reductive group?) and a polarisable quaternionic representation $E$ (ok, this is saying we can write $E =T^*V$, but we don't have a canonical choice of $V$, and we shouldn't fixiate on a choice.)

I don't know what's the difference between $g^{reg}/G$ and $g/G$ (adjoint action). OK, well, if we just do $g/G$, there might be too many orbits (with the same eigenvalues), and picking out $g^{reg}$ is saying, I am looking at the most generic (?) guy with this eigenvalues.

Why we call this integrable structure “Toda integrable system”. I thought it is like Hitchin integrable system, because we are taking eigenvalues of a matrix. Who is Toda, and what did he do? What's 'inverse scattering method'?

OK, let's not be distracted.

The 'reconstruction' result, you mean the gluing two copies method? , is from the 2d gauge theory interpretation. (what do you mean by that 2d gauge theory moduli space?)

The hook question: if you know Floer homology with Lagrangians is categorifying the intersection of middle dimensional homology cycles (quantum homology?)

wait, do we have a notion of product in the decategorified case? Wow, previously, you have access to each individual intersection points, so you can say who talks to who. if you only remember the intersection number, you don't have enough structure!

Read Auroux, Perutz, Weirheim