# Open conjectures on the Fukaya category

This is ported from mathoverflow question https://mathoverflow.net/q/263693/.

Can somebody give examples to open conjectures on the behavior of the $Fuk(M,ω)$ (that's the "mathematical A-model category of D-branes" in physics language) that come from string theory and can be phrased in a mathematically (semi)-rigorous way?

Two examples I know of are Kontsevich's co-sheaf conjecture, and the connection between Deformation quantization and the Fukaya category in Bressler and Soibelman, Nadler and Tsygen. I was wondering if there are more lurking about...

• To the close voters who voted to migrate this to math: I could see closing this question for too broad, since it asks for an open-ended list of examples, but it seems firmly about mathematical physics to me and hence not off-topic here. If you think this should be off-topic here, please do not vote to migrate (since this would send the question to math.SE when it already exists on MO), but vote to close with a custom reason. – ACuriousMind Jun 15 '17 at 17:43
• This post is discussed in the Phys.SE chat room around here. – Qmechanic Jun 16 '17 at 8:56