| Abstract: |
Recently, gluing methods appeared in proving Homological Mirror Symmetry(HMS). The main challenge is gluing Fukaya categories of local pieces. In this talk, working on very affine hypersurfaces, I will illustrate two gluing methods for wrapped Fukaya categories: One is sectorial descent, cosheaf property, developed by Ganatra--Pardon--Shende. It enables us to reduce HMS for very affine hypersurfaces to finding suitable Weinstein sectorial covers, which was discussed in arXiv:2310.10084 based on arXiv:2312.17604. The other is Zariski descent, sheaf property, explored by us in a revised version of arXiv:2303.06955v2. If time allows, I will also illustrate how to apply the latter to prove HMS for complete intersections. My talk will be elementary so that one can follow without knowing wrapped Fukaya categories. |
