Lagrangian correspondences and their local geometry.

Lagrangian correspondences are crucial tools in various branches of mathematics and physics, including geometric quantization, mirror symmetry, and the theory of Fourier integral operators. This paper provides a detailed investigation into the local geometry of Lagrangian correspondences. The authors develop new techniques for analyzing their structure and properties, offering a deeper understanding of how these correspondences relate different symplectic manifolds. The findings can be applied to problems in mathematical physics and have potential implications for developing new computational methods in areas such as wave propagation and signal processing.