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Abstract: In defining symplectic invariants such as Gromov-Witten invariants or Floer homology, a crucial step is the construction of the virtual fundamental cycle or the virtual fundamental chain (VFC). In this highly involved procedure, one typically needs the so-called "gluing construction" to obtain local charts. It was Tian who firstly noticed that to construct VFC in situations such as Gromov-Witten invariants, one does not necessarily need gluing. In this talk, I will review the VFC construction in Gromov-Witten theory and briefly explain Tian's idea. Then I will show how to apply this idea to define virtual counts of pointlike instantons in gauged linear sigma model. This talk is based on the joint work with Tian.

(Edit: This talk is postponed until the speaker gets over a cold.)