Categorical and Enumerative Aspects of Mirror Symmetry: A Tribute to the Life and Work of Professor Bumsig Kim: 5 (KIAS Springer Series in Mathematics, 5)

This open access book is a tribute to the profound contributions of Professor Bumsig Kim in the field of mathematics, particularly in the realm of mirror symmetry.Mirror symmetry is a fascinating duality between complex/algebraic geometry and symplectic geometry, manifesting in various ways.One of the foundational examples of this duality is the comparison of period integrals on a complex manifold with curve counts (enumerative invariants) on its mirror.This vision was ultimately realized through the Quasimap Wall-Crossing Formula, developed by Bumsig Kim and his collaborators. The book delves into the methods for counting curves, including Gromov-Witten theory and Fan-Jarvis-Ruan-Witten theory.In his final works, Kim and various groups of collaborators achieved methods for counting curves on gauged linear sigma models, effectively unifying Gromov-Witten and Fan-Jarvis-Ruan-Witten theory.This monumental effort involved constructing categorical frameworks and developing a dictionary bet