Seminar | Institute of Mathematical Sciences
Working group on Fukaya categories
Time：14:00-15:00, April 3, Wednesday
Location：Room 302, Library
Speaker: Yosuke Imagi, ShanghaiTech University
Abstract: There is an established technique of constructing some degenerate solutions of nonlinear PDEs, called the gluing technique and applied to various circumstances - going back at least to Taubes' work about 1980 in Yang-Mills gauge theory, and used still nowadays by some of our colleagues:
1) https://arxiv.org/abs/1807.09367 by Ruobing Zhang, Sun Song and others, given an explanation by Song last year;
2) https://arxiv.org/abs/1703.09201, https://arxiv.org/abs/1709.09564 by Tim Talbot, given an explanation by himself last year;
The gluing technique for some PDEs (those in gauge theory and of pseudoholomorphic curves) is now a foundation of the notions of Floer homologies and Fukaya categories.
The gluing technique is in essence a parametrized version of the implicit-function theorem which is however applied in different manners to different circumstances. I will explain it in a simple case; or more specifically, I will speak about Section 7.2.2 of The Geometry of Four-Manifolds by Donaldson and Kronheimer, relevant to Taubes' work.