On gauged linear sigma model and related problems

Gauged linear sigma model was proposed by Witten in the early of 90's to explain the mirror symmetry phenomenon and the CY/LG correspondence conjecture. In this lecture, I will firstly formulate the mathematical framework of the GLSM, and then describe an algebraic way to construct the quantum invariants of GLSM in narrow case (for general gauge group) via quasimaps. This was a joint work with Jarvis and Ruan. Finally I will report the recent progress in this field and related problems.