In [this][1] MO question it is stated that there is a relation between some aspects of condensed matter physics (namely the fractional quantum Hall effect) and the algebraic geometry of Hilbert schemes.

Having made a quick google search without immediate results, I'm curious to know:

> 1. How does this interaction between the two topics happen?

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Let's have a more general look. I'm aware of the relation between Hilbert schemes -and also other kinds of moduli spaces of sheaves- and *instantons*. Anyway, here I would be interested to know of other examples more in the vein of the MO question linked above.

> 2. Do moduli spaces in the sense of algebraic geometry -of which Hilbert schemes are a special case- have any link with physics (**except** string theory, high energy and elementary particle physics)?

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Last but not least:

> 3. What about moduli spaces and applied mathematics?

 

 


  [1]: https://mathoverflow.net/questions/231097/reference-request-for-hilbert-schemes?noredirect=1#comment571828_231097