Advances On Complex Lagrangians, Integrable Systems And Quantization

Advances on Complex Lagrangians, Integrable Systems and Quantization explores the rich interplay between geometry, analysis, and mathematical physics, with a central focus on Hitchin systems and the intricate structures of moduli spaces of Higgs bundles and flat connections. Bringing together modern perspectives, the volume reveals how classical geometric ideas — such as spectral curves, Lagrangian subvarieties, and integral-affine structures — resurface in quantum and analytic settings, including Stokes phenomena, oscillatory integrals, and exact WKB analysis.Developed in connection with a collaborative research initiative, this collection highlights a dynamic and interconnected range of themes. These include generalized and twisted Higgs fields, spectral correspondences, hyperkähler and semi-flat asymptotics, and mirror symmetry for Hitchin systems, alongside advances in equivariant quantum cohomology and moduli-theoretic approaches to exact quantization. Each contribution sheds light on deep structural relationships that unify diverse areas of modern mathematics.Rather than serving as a broad survey, this volume offers a carefully curated set of research articles that together capture the current frontier of the field. It is designed for researchers and advanced graduate students seeking both insight into ongoing developments and inspiration for future work at the interface of algebraic geometry, differential geometry, integrable systems, and quantization.