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Now I mentioned before that I am chiefly interested in #GeneralizedComplex geometry underlying all this: All universes that exhibit #MirrorSymmetry are GC, and #branes are GC objects.
However, there is currently no general version for a "GC category of branes". Part of my current work is to define this in certain cases.

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It turns out that #MirrorSymmetry can be described in terms of #branes, which I have described before: For each of the two different mirror geometries, we can define a #category of branes (again, this is very simplified and not exactly right), which is a mathematical structure encoding not only the branes themselves, but also in some sense their interactions. Two universes are mirror if the categories of branes are equivalent in a certain way.

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Today: A short explanation of connections between the different concepts I have talked about:
#MirrorSymmetry is originally an observation from #StringTheory, which can behave the same in different universes with different geometric structures - they are mirror partners. 🧵
#math #physics

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Now, in this particular setting, this does not seem very useful - you can tell what the minimal number of intersection points is by just looking at the picture.
But this is actually just an extremely simple example of a complicated invariant called #Floer #cohomology, which is central to the #math description of #MirrorSymmetry!

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A huge research area in modern symplectic geometry is #MirrorSymmetry, which originally comes from #stringtheory. Very simplified: If two manifolds (="universes") are mirror partners, string theory behaves the same in both, even though they look very different at first glance.
Mirror symmetry involves relating the symplectic geometry of one universe to the complex geometry of the other.