Live on open problems in field theory. In the last live, we discussed a few problem in extending some of our findings to field theory, including the problem of what is the right way to extend state counting measures and entropy to that settings.
Closing various conjectures. I have worked more on ensemble spaces closing conjectures, either proving them or disproving them. First of all, since JSD/MS convergence is not enough to make the entropy converge, the topology is NOT generated by the JSD/MS. Added an open problem on completeness: how can the notion from TVS be generalized to convex spaces? Cleaned up the connection between statistical quantities and the topology they generate. Added a notion of bounded sets for convex spaces (that recovers the one from TVS) and proved an equivalent characterization, closing a conjecture that was open for a long time. Also: infinite dimensional spaces are NOT bounded… though I think we can prove that all finite dimensional ones are.
And I am behind in may other things, because I am getting distracted by trying to close open conjectures…
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