For fun I spent an hour seriously thinking about sheaves of open games. I got way over my head very, very quickly - and that's not even getting to the part with the sheaves or the other part with the PDEs
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Basically the simplest possible example (with one player and time as the base space) is the Hamilton-Jacobi-Bellman equation. Which, so far, I'm failing to get my head around
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Replying to @_julesh_
Difficulty to interpret as a sheaf or to intuitively grasp in it‘s own right?
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Replying to @SandMouth
Just trying to understand the thing itself. If I'm thinking about open games in the right way then I think it will either automatically be a sheaf, or (probably equally likely) the whole thing is a bust
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Replying to @_julesh_
Have you considered the discrete state space version or do you really need the continuous PDE? The PDE form is rather confusing to me. The discrete Bellman equation feels clever but reasonable and has the PDE as a limitting case.
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Replying to @SandMouth
Ah, that's a good idea, maybe I should look at discrete space continuous time first, that sounds way easier if it's a standard thing
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Replying to @_julesh_ @SandMouth
Sadly, Kohn and Serfaty use continuous space, discrete time. It would be interesting to see something written the other way around though!
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Replying to @blockspins @_julesh_
Is kohn and serfaty a mental touch stone? I’m not familiar with it
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bgc Retweeted bgc
Ah, sorry, see this tweet elsewhere in this thread treehttps://twitter.com/blockspins/status/1177274861644918787 …
bgc added,
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