Birational Transformations, Toric Calabi-Yau 4-folds and 2d (0,2) Quiver Gauge Theories

Explore the intricate connections between algebraic geometry and theoretical physics in this conference talk that examines birational transformations of toric Calabi-Yau 4-folds and their relationship to 2-dimensional (0,2) quiver gauge theories. Delve into advanced mathematical concepts including toric geometry, Calabi-Yau manifolds in four dimensions, and the sophisticated interplay between geometric transformations and quantum field theory structures. Learn how birational maps between these special geometric spaces correspond to physical dualities in supersymmetric gauge theories, providing insights into both pure mathematics and string theory applications. Discover the role of quiver diagrams in encoding the gauge theory data and understand how geometric operations on Calabi-Yau spaces translate to field theory phenomena. This presentation, delivered at the ICBS2025 conference by BIMSA, offers a deep dive into cutting-edge research at the intersection of algebraic geometry, differential geometry, and mathematical physics.