Title: Quantum McKay correspondence via gauged linear sigma model

Speaker: Dr. Ke Huazhong (Tsinghua University)

Time: 11:20-12:20 am, May 23 (Thursday)

Abstract: In the early 90's, Witten introduced the gauged linear sigma model (GLSM) to study the phase change phenomenon in string theory. Mathematically, we can interprete GLSM as a symplectic reduction, in which charge vectors play an important role. For a local Calabi-Yau $X$, we can use its charge vectors to describe the moduli space of mirror curves, and hence determine the genus-zero (closed) Gromov-Witten invariants. Similar picture also holds for open string invariants. It is observed that for different limit points in the K\"ahler moduli of $X$, it is better to use different charge vectors, which are all $\mathbb Q$-bases of the lattice of invariants. Following this idea, we have proved the quantum McKay correspondence for disc invariants of effective outer legs in semi-projective toric Calabi-Yau $3$-orbifolds with respecto to Aganagic-Vafa branes, using the recent result of Bohan Fang, Mellisa Liu and Hsian-Hua Tseng. This is joint work with Jian Zhou.