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Charlotte Kirchhoff-Lukat<a href="https://mathstodon.xyz/tags/TodaysMath" class="mention hashtag" rel="tag">#TodaysMath</a> 2/2: The appropriate <a href="https://mathstodon.xyz/tags/Floer" class="mention hashtag" rel="tag">#Floer</a> <a href="https://mathstodon.xyz/tags/cohomology" class="mention hashtag" rel="tag">#cohomology</a> theory to associate to (composable) Lagrangian correspondences is *quilted Floer cohomology*. I like this paper by Wehrheim and Woodward to learn about it: <a href="https://arxiv.org/abs/0905.1368" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://arxiv.org/abs/0905.1368</a>

Charlotte Kirchhoff-Lukat<a href="https://mathstodon.xyz/tags/Reference" class="mention hashtag" rel="tag">#Reference</a> request: I am attending a learning seminar on <a href="https://mathstodon.xyz/tags/Floer" class="mention hashtag" rel="tag">#Floer</a> <a href="https://mathstodon.xyz/tags/Homotopy" class="mention hashtag" rel="tag">#Homotopy</a> theory this semester. Coming from the symplectic side of things, I could use a nice accessible reference on the <a href="https://mathstodon.xyz/tags/algebra" class="mention hashtag" rel="tag">#algebra</a> side, specifically on stable ∞ -<a href="https://mathstodon.xyz/tags/categories" class="mention hashtag" rel="tag">#categories</a> and the category of spectra in particular. I already have Chapter 1 of *Higher Algebra* by Jacob Lurie. Anybody have any other good suggestions? (Ideally ones that do not require the whole kitchen sink of model categories.) Thanks in advance! 🙂 :k5: <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="tag">#math</a>

Charlotte Kirchhoff-Lukat<a href="https://mathstodon.xyz/tags/ExplainingMyResearch" class="mention hashtag" rel="tag">#ExplainingMyResearch</a> 23 To start, I am working on 2-dimensional "universes" like the disc with boundary, which are not strictly speaking GC, but similar enough to be useful. My <a href="https://mathstodon.xyz/tags/preprint" class="mention hashtag" rel="tag">#preprint</a> <a href="https://arxiv.org/abs/2207.06894" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://arxiv.org/abs/2207.06894</a> describes how to define <a href="https://mathstodon.xyz/tags/Floer" class="mention hashtag" rel="tag">#Floer</a> <a href="https://mathstodon.xyz/tags/cohomology" class="mention hashtag" rel="tag">#cohomology</a> for so-called log-<a href="https://mathstodon.xyz/tags/symplectic" class="mention hashtag" rel="tag">#symplectic</a> surfaces. I am currently finishing off the full description of the category of branes in this setting, so keep your eyes open! 🙂

Charlotte Kirchhoff-Lukat<a href="https://mathstodon.xyz/tags/ExplainingMyResearch" class="mention hashtag" rel="tag">#ExplainingMyResearch</a> 17 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 and mentally "smoothing out" the wiggles in the middle - the minimal number is either 0 or 1. But this is actually just an extremely simple example of a complicated invariant called <a href="https://mathstodon.xyz/tags/Floer" class="mention hashtag" rel="tag">#Floer</a> <a href="https://mathstodon.xyz/tags/cohomology" class="mention hashtag" rel="tag">#cohomology</a>, which is central to the <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="tag">#math</a> description of <a href="https://mathstodon.xyz/tags/MirrorSymmetry" class="mention hashtag" rel="tag">#MirrorSymmetry</a>!

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