Show threadCharlotte Kirchhoff-LukatMar 3, 2023
#TodaysMath 2/2: The appropriate #Floer #cohomology theory to associate to (composable) Lagrangian correspondences is *quilted Floer cohomology*. I like this paper by Wehrheim and Woodward to learn about it:
https://arxiv.org/abs/0905.1368
Floer Cohomology and Geometric Composition of Lagrangian Correspondences

We prove an isomorphism of Floer cohomologies under geometric composition of Lagrangian correspondences in exact and monotone settings.

arXiv.org
Charlotte Kirchhoff-LukatFeb 9, 2023
#Reference request: I am attending a learning seminar on #Floer #Homotopy theory this semester. Coming from the symplectic side of things, I could use a nice accessible reference on the #algebra side, specifically on stable ∞ -#categories 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! 🙂 
#math
Show threadCharlotte Kirchhoff-LukatDec 9, 2022
#ExplainingMyResearch 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 #preprint
https://arxiv.org/abs/2207.06894
describes how to define #Floer #cohomology for so-called log-#symplectic surfaces. I am currently finishing off the full description of the category of branes in this setting, so keep your eyes open! 🙂
Log Floer cohomology for oriented log symplectic surfaces

This article provides the first extension of Lagrangian Intersection Floer cohomology to Poisson structures which are almost everywhere symplectic, but degenerate on a lowerdimensional submanifold. The main result of the article is the definition of Lagrangian intersection Floer cohomology, referred to as log Floer cohomology, for orientable surfaces equipped with log symplectic structures. We show that this cohomology is invariant under suitable isotopies and that it is isomorphic to the log de Rham cohomology when computed for a single Lagrangian.

arXiv.org
Show threadCharlotte Kirchhoff-LukatDec 6, 2022
#ExplainingMyResearch 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 #Floer #cohomology, which is central to the #math description of #MirrorSymmetry!