Quantum $K$-theory and $q$-Difference equations

Abstract

This is a set of lecture notes for the first author's lectures on the difference equations in 2019 at the Institute of Advanced Study for Mathematics at Zhejiang University. We focus on explicit computations and examples. The convergence of local solutions is discussed.

arXiv commentIn this version, we added a reference of Garoufalidis-Scheidegger (arXiv:2101.07490), and fixed some errors

References in corpus (6)

• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories
• Reconstruction and Convergence in Quantum $K$-Theory via Difference Equations
• Difference Equation for Quintic 3-Fold
• Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry
• Confluence of quantum $K$-theory to quantum cohomology for projective spaces

Cited by in corpus (1)

• Difference Equation for Quintic 3-Fold