3 d mirror symmetry is a program of the general extension from 2 d mirror symmetry.
In this subject, hyper kaehler geometry plays the major role relating to the holomorphic Morse theory.
This concept is also physically interpreted in terms of the Coulomb branch and Higgs branch with the symplectic duality.
Furthermore, it is related to the relative Langlands with the spherical varieties in the arithmetic geometry.
We will mostly follow the articles,
1. 3D mirror symmetry is mirror symmetry by Ki Fung Chan and Naichung Conan Leung)(arxiv. 2410.03611)
SYZ mirrors in non-abelian 3D mirror symmetry, by the same authors (arxiv. 2408.09479)
2. 3-dimensional mirror symmetry by Ben Webster and Philsang Yoo (arxiv. 2308.06191, AMS notice, October, 2023)
3. Holomorphic Floer theory 1 by Maxim Kontsevich and Yan Soibelman (arxiv. 2402.07343)
4. Relative Langlands Duality by David Ben-Zvi, Yiannis Sakellaridis and Akshay Venkatesh (arxiv. 2409.04677)
