Explore the intricate connections between moment maps, nonlinear partial differential equations, and stability concepts within the framework of mirror symmetry in this 54-minute conference talk delivered at ICBS2025. Delve into advanced mathematical concepts as the speaker examines how moment maps serve as crucial tools for understanding geometric structures, while investigating the role of nonlinear PDEs in describing complex mathematical phenomena. Discover how stability theory applies to mirror symmetry, a fundamental concept in algebraic geometry and theoretical physics that relates different geometric spaces. Gain insights into cutting-edge research that bridges differential geometry, algebraic geometry, and mathematical physics, with particular emphasis on the analytical techniques used to study these sophisticated mathematical relationships.