Explore the intricacies of the Fukaya-Morse A-infinity category in this advanced mathematics lecture delivered by Pavel Mnev at the Galileo Galilei Institute. Delve into the complex interplay between Fukaya categories and Morse theory, examining how these concepts intersect to form a powerful framework in symplectic topology. Over the course of 75 minutes, gain insights into the structure and properties of this sophisticated algebraic construct, its applications in modern mathematical research, and its implications for understanding geometric and topological phenomena. Engage with cutting-edge ideas at the forefront of mathematical inquiry, suitable for graduate students and researchers in the fields of algebraic topology, symplectic geometry, and related areas.