Akishi Ikeda, Josai University, Saitama, Japan, and Yu Qiu, Tsinghua University, Beijing, People's Republic of China, and Beijing Institute of Mathematical Sciences and Applications, People's Republic of China

Description
Chapters 1. Introduction 1. Categorical Part 2. $q$-Deformation of stability conditions 3. Topological Fukaya categories 4. Deformed Calabi-Yau-$\mathbb {X}$ completion 5. $q$-Deformation of topological Fukaya categories 2. Geometric Part 6. Quadratic differentials on Riemann surfaces 7. $q$-Deformation of quadratic differentials 8. $q$-Stability conditions via $q$-quadratic differentials 3. Applications 9. Bridgeland-Smith theory on Calabi-Yau-$N$ categories 10. Hurwitz spaces via quadratic differentials in genus zero 11. Almost Frobenius structures for stability conditions: ADE case